Sorry, a couple more thoughts...
With all of that being said, you really won't hurt much by putting a dead shrimp into your aquarium for however long you like. You will have excess nitrate at the end of that period (that's what ammonia and nitrite eventually become), so you will need to do a water change that you likely wouldn't have done otherwise. I can't really decide whether having a foul environment rich in ammonia and nitrite would be toxic to microfauna that would ordinarily populate as the aquarium develops. I guess if something survived the live rock curing process, it should probably survive a tank polluted with decomposing shrimp.
As for algae, your tank should have some algae growth- every productive ecosystem does. The right mix of clean up crew will help, and that's a good opportunity to get some bioload. Also algae wiping, water changes, and good feeding habits will keep it looking clean. Many people leave their lights on for too long. Corals only need about 4 hours of light to meet their photosynthetic needs (some people say even less!). Any more than 4 hrs just adds to your enjoyment, but it will cause more algae growth.
Sorry about the second post, good luck with your tank!