I have sudocreme too. Might use that in the day when he is awake a bit more, and I can check he doesn't touch it, then put it in his mouth.
Just put it on really thinnly and it shouldn't be a problem. My DS also gets a dribble rash around his mouth. I went to the chemist looking to get something for it and they told me that the zinc cream was the best thing for it. I was worried about him ingesting it, but they told me as long as you spread it really thin it won't be a problem.