I don't have much experience with sinew bowstrings, but my first thought was "why would you want it limber and not dried out?". water causes sinew to stretch, not a quality you want in a bow string. Dry may be stiff, but i don't see a problem with the stiffness. I don't think sinew will weaken if dried out. You may want it damp in order to tie good knots in each end, but once that is done, i think a stiff dry string would work fine. I have one siew bowstring, which i hardly use, but it is dry and stiff as a wire but works fine.
good luck