No. The "these purposes" it's referring to there are for purposes of transferring and adding runes and upgrades. Handwraps are not weapons, they are an item that can have weapon runes put on it, and whose effect is to give your unarmed attacks the effects of those runes.
I will say, ask your GM about reflavouring the handwraps as tattoos if you want that. As a GM I'd allow it. I'd just want to make sure there is some way of "confiscating" the item, but for example you could say that if the tattoos are covered up then they lose their power or something like that.