Cleaning of Exterior of Outdoor Camera

A few months ago I noticed a number of false reports on my outdoor camera within a 48 hour period. After checking it the first day and not finding anything, I again checked it the 2nd day to discover two lovely little swallows had decided the top of my camera was the perfect location to build their nest. With it not covering the camera, and not compromising my view, I decided to just live with the false reports while the birds raised their family and figure out the rest later. 

The camera was a little trooper and kept going greatly until the battery finally gave up the ghost and needed to be charged. I did not what to disturb the nest until I was absolutely sure they had finished and abandoned it once the little chicks were capable of flying. 

Well, now that it's abandoned I can survey the situation and while the camera still looks fine, it's got a large nest glued to it with mud and a whole lot of bird poop all over its top (thankfully the camera's angle prevented anything from getting on the lens area). So I've got a cleaning job ahead of me but after looking around, I couldn't find any good solutions on the best way to do a "deep clean" on the camera. Most references to cleaning are just related to the lens and using a warm rag with some soap, but those solutions aren't going to work necessarily with the amount of material attached to the camera. 

While the cameras are outdoor rated (obviously) are they water proof? or just water resistant? I'm hesitant to completely submerge the camera (sans battery) as that seems like a bad idea but are there any suggestions other than just to roll up my sleeves and scrub with a brush over a bath of warm water?