If walk/trot classes are an option, go for it! Showmanship can be fun if you like the precision of pattern work. Show ring trail generally has cantering/loping (unless you find W/T classes,) and competitive trail is likely going to be very hard on joints with all the obstacles, hills, etc.
If you can be content learning new skills outside of the show arena, maybe work towards getting him so good at guiding with your legs & weight that you don't need hands and could essentially ride bridleless? Get him doing patterns without using your reins - cones, poles, barrels, figure eights, serpentines, perfectly round circles, straight lines. Work on perfecting walk-trot, trot-walk transitions. Be able to extend or to slow his trot. Get him to stop and back or do a 360° turn. A responsive, well-trained horse is a joy to work with, no matter the speed he's traveling :)