The 15" shaft may actually work even without a bracket, but it will be prone to rolling out of the water in waves. I'd skip the adjustable bracket, and instead get a fixed height bracket. It will be less costly and will be less "ungainly" looking on the boat. Those adjustable brackets are overkill on a small, low freeboard boat like a DS III, the motor ends up looking like it is hanging out in mid-air when the bracket is lifted. With a fixed-height bracket, mounted so that the top of the motor-mounting board is just even with or slightly lower than the top of the transom, should keep even a short-shaft motor in the water most of the time it is running. As the water flow breakes clear of the bottom of the transom, it rises up and so mounting a motor the distance away from the transom that the fixed bracket does will actually put the propeller lower in the water than if the motor was clamped right to the transom. I have my outboard clamped to a board bolted to the transom (to get the angle of the motor more vertical) and that works fine on my DS II, and the motor lower unit is clear of the water most of the time, and even if not..... isn't creating enough drag to worry about. Powerhead is always well above the water.
I have seen more than a few long-shaft outboards in the 2-4 hp size listed on e-bay, and it is worth checking Craigslist or local classified ads for listings. A long-shaft engine (new or used) will usually cost a lot less than the cost of a short-shaft engine plus bracket. I have a 4hp Johnson (2001 2-stroke) on my DS II, it is slightly more power than I really "need", but it is nice to have that extra oomph at times. A 2hp will push a Day Sailer quite well, if you can get the right prop! I had a 2.3 hp Johnson that pushed the boat OK, but it was obvious that the prop was not ideal and so I never really got the full power available. My old 2 hp Johnson (used on our 8' dinghy) that I tried once actually seemed to have more power than the 2.3 hp.
