I don’t even remember the detail that he had a blaster. Did he end up using it on something?

If I were in that situation, I’d consider:

1) If I’m captured and in the power of a mad person who is making me face a monster in an arena, and I just shoot it with a concealed weapon, I’d think they might be so upset (and concerned that I’ve got a ranged weapon) that they decide to kill me then and there. So I’d only use it if I thought it was my only option, and/or if I thought I could escape/survive or it was my only best hope of getting a better outcome.

2) It might be more useful later, if I can keep it concealed.

@Zaku it is just after Jabba says “I shall enjoy watching you die”. Then Luke uses the force to steal a pig soldier’s blaster.

Your question made me look this up and I have an answer. Luke has the blaster as he falls through the floor but looses it when he hits the bottom of the cave.
https://archive.org/details/return.-of.-the.-jedi.-1983.-despecialized.-720p.x-264.-ac-3.5.1