I can't say that I've done any research on shrimp/cholesterol in particular but I do know that fish, in general, have what is considered a "good" cholesterol that eats away at the bad cholesterol in a person's system. Omega-3 fatty acids are what they are called. Of course, I think a lot of this also depends on the way the shrimp, or any seafood/fish for that matter, is cooked. Baked or broiled without breading or batter is best. Personally, I've never liked shrimp unless it is battered and it's kind of difficult to make battered shrimp without deep-frying it so that shoots the cholesterol all to heck anyway!
In case you weren't aware, Omega-3 fatty acids are available in an over-the-counter supplement in the vitamin aisle of any discount store - Wal-Mart, Target, K-Mart, and are also available over-the-counter in pharmacies but I think you pay more for them in a place like that. They'll either say "omega-3 fatty acid" or "fish oil" tablets.
As another aside note, my husband had a cholesterol problem and before he would start medication he told his doctor he wanted to try fish oil tablets and it did help to reduce his cholesterol a little bit.
EDIT: Omega-3 fatty acids have also been shown in clinical studies to increase one's brain function, particularly memory. Some doctors are recommending daily omega-3 supplements to Alzheimer's patients.
I'm not trying to be a smarty pants by offering all this information. It's just that I used to be a medical transcriptionist before becoming a stay-at-home mom and so I've heard a lot about stuff like this.