Shrimp are indeed very sensitive to copper. It is the fastest way that I know of to kill most invertebrates.
I don't see where you said how big the tank is, but even a 5 gallon could hold a betta and a small number of pygmy cories to give him company and distract him from biting his tail.
I don't see where you said how big the tank is, but even a 5 gallon could hold a betta and a small number of pygmy cories to give him company and distract him from biting his tail.

what condition is he's tail in...