Per advice of my taxidermist I've used Baby Oil on my shoulder mount once a year since 1976. I apply it on my hand going the direction the hair lays. Then I comb the hair with a fine tooth comb. I do all the hair except inside the ears. I use a liberal amount on the nose and clean the eyes with a dry cloth. The mount looks almost as good as the day I picked it up 36 years ago.

I'd think wetting the hair would work to get it to lay. Once it lays you could use the Baby Oil. But, things have changed in the taxidermy world since 1976, so you may want to consult a taxidermist before using what I have..