Re: motor size?
Too many unanswered questions here. First of all, you need to find out what the capacity plate says. Not only for safety reasons, but legal liability as well. You should not overpower the boat. Contact the manufacturer. If the boat is real old and they are not in business, google the ACBS or Fiberglassics or other sources to find out old specs.
A 48" beam sounds awful small for a 15' boat. A 20 hp may be too big.
I am assuming that a 20 Yami is a 4-stroke. Thats a pretty heavy motor. That in itself may be too much weight for the old transom.
Looking at your picture, it looks like that's a short shaft transom. Better check that out too. Yami does make a 15" 20 HP, but they are few and far between. Most dealers stock only long shafts.
Two years ago I upgraded from a 15 to a Yami 25 (2-stroke) on my 14' aluminum boat with a 67" beam. It was wayyyyy too much power and I ended up upgrading the boat next....LOL.