Ideally, the alcohol will seep into the same places the Gatorade did, so unless you were really serious about cleaning, you shouldn't try to disassemble. I've disassembled compact cameras before, to replace LCDs; a Canon ixus and a Panasonic Lumix. I've been successful at the latter and failed at the former. So you do run a risk.

If you just put a small amount of alcohol in the same place the Gatorade went, it should get in there I think. At first it will just liquefy the dried sugars and salts, which will then dry in place again and it will get sticky again. But if you do it enough times, I think it will break down those contaminants enough to make things function.