I certainly had no intention of putting this young man into a 10" hat. I firmly believe in the power of proportion. I believe finding a reasonable crown height on a top hat would not look out of place both in scale and propriety.
I think the shorter the top hat the better for him, and a top hat would look dapper with a tailored vintage-looking dinner jacket. As others have pointed out, plenty of different hat styles were worn. The side effect of trying to make your friend look taller with a taller hat is that you could make his smaller body look like it has a huge head, so that's something to consider.
To give you and your friend an idea of what he would look like in a top hat, you might take advantage of the Halloween season. It might be worth stopping by a costume store and seeing if they have different height top hats. Sure, they will look ridiculous in style, but it beats buying a $150 vintage top hat just to find out it doesn't look good on him.