BotW has a difficulty scaling mechanic running in the background at all times. The moreenemies you kill, the more the world around you will level up: enemies turning into higher-ranked individuals, weapons turning into better variants, boosts / bonuses like extra attack power or extra durability ... this mechanic was made to provide the player with both a constant challenge and better equipment over time.

However, this also means that some of the low-level stuff will become increasingly more hard to find the more you progress, as some of that stuff goes nearly extinct. Traveler's Swords for example are a dime a dozen if you just started playing the game, but once they upgraded to Soldiers Swords, it will be very hard to find one just lying around. And the Sheikah Sensor Plus is even more of a hindrance than a help in this case, since it reacts to all of the Traveler's Swords carried by NPCs, which are useless for this quest. (You can't take them, and "just" a picture isn't enough for Nebb)

... and since Nebb is a picky little pain in the neck, he will NOT accept the better weapons. If he wants to see a Moblin Club and you bring him a Spiked / Dragonbone Moblin Club, he'll simply ignore it. It has to be the regular, boring, low-level variant, otherwise the quest won't advance.

The weapons Nebb wants to see, in order:

Traveler's Swords scale up pretty early. Most "Traveler's" equipment inside of chests, held by enemies and even some of the ones just lying around in the overworld will eventually turn into better/stronger variants (Soldier > Knight > Royal) so the "Traveler" tier will be hard to find then.

An easy spot to find a Traveler's Sword that doesn't scale up (but respawns every Blood Moon) is Kakariko Village. If you enter the village from the south, there is a tiny bridge after the first tree, and to the right of that bridge is a Traveler's Sword submerged near the waterfall. You need Magnesis to fish it out.

The Fire Rod and Moblin Club can be found at the northern end of the Digdogg Suspension Bridge just west of the Great Plateau - you can nearly glide there from the Cryonis Shrine.

There are 3 red Moblins carrying regular Moblin Clubs and neither the monsters nor their equipment scale up, so they will carry the low-level clubs even late-game, after other enemies turned silver/golden already. In Master Mode, these Moblins are blue instead of red, but still wield un-upgradable regular Moblin Clubs.

That area also has a burned-down house with a Fire Wizzrobe dancing above it. Fire Wizzrobes can be OHKO'ed with frost attacks (like Ice Arrows) so you can easily oneshot it pick up the Fire Rod afterwards. The Fire Wizzrobe is a Meteo Wizzrobe in Master Mode, but will still wield a regular Fire Rod.

Duplex Bows and Windcleavers aren't exactly hard to find after you have defeated Master Kohga and retrieved the Thunder Helm, since you'll be constanly ambushed by Yiga Archers and Blademasters for the remainder of your playthrough. But RNG can also be a pain when you WANT to be ambushed and they just don't appear... and that's where the "guaranteed" locations are useful.

In front of the Yiga Hideout, there are 3 stationary Yiga Footsoldiers, all equipped with Duplex Bows, and two more archers are hidden a bit further up the canyon. It isn't exactly an easy-to-reach spot and fighting 3 enemies at once can be a hassle, but one charge of Urbosa's Fury will get rid of them, and all of them respawn every Blood Moon. There is no RNG involved - they're guaranteed to ambush you if you try to enter the Hideout.

In Master Mode there are also regular enemies with Duplex Bows, like for example a blue Bokoblin near Proxim Bridge. Since that Boko is a "lookout" enemy, headshots will deal 10x damage so it's easy to OHKO him.

For a Windcleaver there is a Yiga Blademaster guaranteed to appear during the "Stolen Heirloom" quest. If you can make him drop his weapon during the fight, you are usually able to pick it up after the cutscene. If you can't immediatly find it, use Magnesis to look around. Unlike the other foes so far, this one does NOT respawn.

The Blademasters inside the Yiga Hideout are very dangerous since they will kill you in a single hit even with Mipha's Grace / Fairies and they will also call all of their buddies to gang up on you, so fighting them head-on is a bad idea. And if YOU kill them with a sneakstrike or Ancient Arrow (the only things guaranteed to silently OHKO them), they will disappear without leaving their weapons behind.

In Master Mode there is a chest on a floating platform near Mikau Lake in Zora's Domain, guaranteed to contain a Windcleaver. But since these chests never respawn once you looted them, it is a one-time-only type of deal.

Additional information: There seems to be an issue where the Blademasters just don't drop their Windcleavers if you kill them "the wrong way", but I have not yet fully figured out what you have to do to guarantee a drop. Whenever I killed them using just Urbosa's Fury and/or bombs, they only dropped bananas and rupees. If I kill them with melee weapons, they seem to drop their Windcleavers pretty consistendly, but also not every single time (unless I'm doing something wrong).

The Ancient Battle Axe+ is a bit annoying again - it HAS to be the variant with a single (+) at the end, not the (++) variant or the one without a plus sign. And the only way to get those, is from the Guardian Scouts III inside the Modest Test of Strength shrines. Luckily, all of these enemies respawn every Blood Moon.

3 shrines where you could get that weapon are Ke'nai Shakah Shrine, Namika Ozz Shrine and Muwo Jeem Shrine. In all 3 cases, you have to defeat the Guardian Scout, otherwise they won't drop their equipment.

In Master Mode, these Guardian Scouts are ranked up to GS-IV but they will still have the same type of equipment.

Halfway between Warbler's Nest and the Fight Range, there is a skull camp with a couple of Bokoblins inside. One of them is a black Bokoblin holding a Frostspear and if you don't feel like fighting, you can just shoot a couple of shock arrows into the camp and snatch the spear while the enemies are stunned.

Once you completed all 4 Divine Beasts, the enemies inside the Coliseum Ruins will also have elemental equipment, and one of the Lizalfoes will have a Frostspear. This might be the easier-to-reach place (and doesn't require cold res) but it will only work after all 4 Divine Beasts have been freed - otherwise, the foes will have regular metal equipment.

The last weapon Nebb wants to see is the Ancient Short Sword and there is only a single place to obtain one - the Akkala Tech Lab. In order to get that sword, you have to unlock the ability to buy weapons in the first place (Blue Flame for the Hateno Tech Lab first, then the same in Akkala again) and then pay Cherry (the robot) 1,000 Rupees, 15 Ancient Springs, 5 Ancient Shafts and 2 Ancient Cores (regular size) while you have at least one empty space in your melee weapon inventory.

There are no other ways to obtain this sword.

Additional information:

Most of the places listed in this guide are not the only guaranteed spots. They're just the ones I personally found the most convenient.

For example, there is a Stalnox in Harfin Valley with a Frostspear stuck in his ribcage, but you have to kill that miniboss in order to obtain the spear, which is a bit harder to do than just shocking the Boko near the Flight Range and stealing his weapon.