I would like to clean & detail portions of my engine bay and I have found the paint comes off easily. Paint comes off with rubbing alcohol (I was putting on a oil change sticker) and NXT wax.
I haven't had paint peel off on me in an engine bay before, however if I were you I would use a mild soap or APC/Degreaser and agitate with a brush. Tedious, yes - however I promise it is less tedious than repainting an engine bay.