The risk of a failed launch and having a nuclear warhead falling on an unintended target isn't negligible, and sending a heavy payload outside of the Earth gravitational pull is quite expensive.
Same reason why we don't send our nuclear waste into space or the sun.
And damaging another planet in our solar system use of little scientific value compared to leaving it as-is.
Personal opinion though: It would be an absurdly expensive way to taint future study of any place we nuke, especially if we want any hope to find any type of life on another planet.
I really hope we find something on Europa or Titan. Both have water and heat, so maybe they’ve got something next to a seafloor vent or something.
All countries have a gentleman agreement not to launch nuclear material into space. If the launch failed, it'd be catrostrophic for people here in earth.
It's really expensive to launch stuff into space, getting stuff out of the earths orbit is another level of power beyond getting it above the atmosphere.
Because we wouldn't be able to see it from that far away. I say we do what you said but for the far away land of Britain and that way we can all enjoy it here on earth ☺️