Shrimp are always a bit of a gamble with any fish, but 90% of the time they'll be fine. I've kept rcs with bettas before with no problem, that doesn't mean your betta won't cause problems. I say give it a try.
and a lot of people suggest trying ghost shrimp first, and even though it can be helpful (because if the fish kill them they'll probably kill any shrimp) it isn't a great method IMO. Lots of time fish will ignore the clear ghost shrimp but they see red and all the sudden it's