Depends on the betta. My betta has always been fine with shrimp, but one day he must have gotten hungry, cause one went missing and all that was left was a shrimp tail. Try ghost shrimp and see if he acts okay with them, and if he does I'd say go for it.
I'd try cherries first as they're colourful and small and therefore easy targets. If he's going to bother about shrimp, he'll bother with those. If he doesn't seem to mind after a few weeks or so, I'd try a few ornamentals - if they go down ok after a while, you could get some more. I'd go slow-ish with it, just to be safe
If the ornamentals don't go down well, you could always try amanos or ghosts, as they're not so colourful - therefore I would imagine they're less likely to be targets.
Crystal reds are a lot more fussy about the water, RCS are a little more forgiving. Also, put lots of plants and create hiding places in your tank, the shrimp have more chances to get away from a hunting Betta!
Also, just a note - watch what shrimp you mix together if you don't want them to interbreed. I think planetinverts has a very good table as to which you can and cannot mix