Put sand, live rock and salt wate rin and let it bump on through the cycle.DO NOT add any dead shrimp. Yur tank will cycle faster and be suitable for fish in no time without half the hassles of smell and poluted water and needing as many water changes, and be better off in the long run as well.
I have cycled tanks from start with nothing but decent live rock and once ammonia and nitrite went to zero added a fish or two, and never ever did a water change and it worded just fine. Even critterson yur live rock will survive that more than likely would have died if a shrimp was added and ammonia and nitrite levels got to high.