Not a teacher
You must know what context this appears in, or it is an ambiguous question. What is the context it is being used in? If it's something you are writing, you would want to be more specific or just write out does.
"What's he like to wear?"
"What's he like on his pizza?"
"What's he like to do for fun?"
I think what does sounds more natural in speaking and writing for the first and third examples though, but that's just me.
If you are asking if you can say "what's" instead of "what does" when speaking, yes you can, but you would want to watch what word you stress and possibly be more specific or you run the risk of being misunderstood.
The original question can go either way if you know the context:
Speaker 1: "Have you met Bob?"
Speaker 2: "No. What's he like?" (what is)
S1: "Help me pick out a gift for Henry."
S2: "Okay. What's he like?" (what does)
In speaking "what's" for what does is a little less formal.