Mate I can't see why it wouldn't work. You just have to find a way to get that copper pipe on REAL tight against the heat as contact pressure has a huge bearing on heat transfer ability. Best thing to do would be to tear the original cooling fins off and get it all smooth then wrap tight as hell.
Give it a go and for a test run just run tap water through the cooling head slowly and it should come out warm to hot
The test run should act something like the cooling muffs people stick on outboard motors when flushing them out.
Another slightly crazy idea is you could actually make a water jacket that goes over the cylinder. Seal it up with something like JB weld and then the water jacket will hold water in as it passes over the cylinder itself
Just a tip though. On a head kitted engine just having a watercooled head would do a lot to help a high compression motor. You also find that in a high performance 2 stroke engine most of the heat build up is contained in about the first 30% of the stroke from top dead centre so even cooling ONLY the head would have the benefit of drawing any remaining heat from the cylinder.
If my memory serves me correctly Porsche at one stage made the transistion on some models where they went from aircooled to watercooled by using an aircooled engine block and then specially developed watercooled heads.. There's no reason the same concept can't work for a 2 stroke engine.
question time! 
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