Yep i would go with a 4 stroke it would be a lot easyer to quiet it down and 50 cc Honda or the 4gt (Honda clone will rev the equivelent of a two stroke 7,800 rpm's.
Also if you want quiet the less chain you have the quieter it will be. You could use a wizzer pully on the rear wheel ( i am going with a 24" bike rim for a pully to the rear,like Harry did in the Villers beach cruser ) The 24" rim would mean you would have to cut the frame for clearence like the Matag Flyer,that big rim would give you a low gearing without to many big pullys or sprokets up front. Thats Dax is in Colorado http://thatsdax.com/
He has helped me a lot with parts for Honda...............Curt