I'm drawing a blank. I'm sure there are examples of the bowcaster being used by someone other than wookies somewhere in Star Wars films. Am I wrong? lol Yes, I remember Han using it briefly in The Force Awakens, but other than that?
Chirrut uses a lightbow in Rogue One, which is a subset of bowcaster - and like Chewie's it's held like a crossbow.
Embo used a bowcaster. He was Kyuzo and a bounty hunter who had a big hat that was a shield/weapon combo. I can’t think of anyone else using a bowcaster besides Han Solo, the rest were all Wookiees.
In KOTOR, you could equip bowcasters on anyone, I believe. Dunno if you want to to count that. Speaking of bowcasters, in the OT we only ever see Chewie use it once on Endor, right? I don't think we ever even get a good look at the thing in the rest of the trilogy.