The Chronic Wasting Disease Alliance has some simple safety precautions that would prevent accidental infection (if such infections are possible).
CWD is caused by a prion, a misfolded protein which is capable of replicating itself by forcing normally folded versions of the protein to refold. If you're a Vonnegut fan, think of ice-9 in Cat's Cradle. The mode of transmission in deer and elk remains unclear, but it's probably dietary, as it is in "mad cow disease," scrapie, and Creutzfeld-Jakob disease. Once it starts spreading, it causes nerve cells to degenerate, leading to the spongy part of bovine spongiform encephalopathy (the fancy name for mad-cow).