Yep use a cooler/icechest. You can buy airpumps that you can run on batteries or clip onto your trolling motor battery. As a matter of fact, Doug Hannon has a huge cooler on his boat that he uses as livewell so he can recondition the bass before releasing them.
Drew, I did this once and used a through hull fittings attached to the cooler. two small bilge pumps to help fill and recirculate the water, a piece of ply wood epoxied to the side of the cooler for the toggle switches and pumps mountings to make it all work. I had to hang the flexable hose over the side to pump the water in and out so the process was all manual, but served its purpose. It was located in rear department of the boat so the wiring was not hard and the hoses did not pose too much of a problem.
I did the same thing, I used to crappie tournament fish, you cannot weigh a dead fish so we used to try every trick in the book to keep our fish healthy. We had the cooler thing going on. Strapped to the back deck of the boat looked like hell, but it works. ( The prop will flat tear up your hose if you don't reel it in when you take off)