Engines can be had. Ask for one on buy/sell. Even if it needs rebuilt it'll be worth it. You can rebuild a bottom end for 30 bucks or less. 6202c3 bearings, a new crank seal, and you can cut a gasket. It'll be like new. Stock top ends tend to be fine as is for running. Just clean it up. Use some copper spray on the base gasket and on the mating surfaces for the head.
It's not hard to rebuild an engine for cheap. And you don't have to upgrade. You can do all that later.
I wouldn't bother putting a bicycle engine on it. You'll find it complicated and difficult to make work correctly, and by the time you're done spending what you need to do it youd be better off with the stock engine. Besides, it'll likely look terrible and be slow unless you are super good at fabrication, and if you were, you could apply those skills to a stock engine easier.
Just my opinion. Stock engine is the cheapest and best route.