I've had two bettas who have lived with red cherries - one didn't seem to mind them, the other killed them within a week. It's very much down to the individual betta when it comes to tankmates. If you'd like shrimp, I'd try some larger ghost or amano shrimp and see how he goes. If all goes fine, you could try some red cherries. Their brighter colour and smaller size makes them more likely to be attacked than the larger ghost/amano shrimp.
Snails usually get along with most bettas, so you could try one of those. A nerite snail, perhaps?