Ghost shrimp are pretty big and much faster than a frog when something is coming after them. I don't think it is unlikely that the betta would kill a frog. Bettas can kill each other, other fish, and without a doubt a defenseless frog. I, personally, would not try to put a frog in there unless you have the time to watch every second and have a separate tank waiting for the frog if it doesn't go well. I suggested a snail because they move slowly enough that I think a lot of bettas consider them to be migrating rocks or something, and leave them alone. But either way, watch your betta's reaction carefully and be ready to intervene.
Also, how is the cover in your tank? Are there a lot of plants/nooks that provide hiding places?