Any bow will work, but it's way more convenient to have a dedicated bow, regardless of whatkind you choose.
For deer, I like the holding time and power of a compound, but for fish, I prefer a recurve. My current fishbow is a45# fiberglass P.O.S.

, and it does fine. Very light, which is good, because I will rarely set it down in hours of fishing. I'll replace it eventually since I had to rig it for a reel mount since it doesn't have predrilled holes for anything, and no place to drill new holes.
I also have an old 50# compound for fish, but it's just my backup/loaner.
In bowfishing, the situations where compounds really seem to have an advantage are on very deep fish where you need extra penetration, and in very murky water where the carp are swirling up the mud so bad that you'll only see a part of the fish for a second or two at time so you will want to be holding your draw and waiting until he shows himself.