Well, a coaster brake can be converted to work by hand...or you could just get a drum brake which is designed to work that way to begin with.
The chain from the sprocket up to the handlebars idea is no good. The weight of the chain and all the whipping around it would do while riding would require a really heavy spring pressure to keep it taught, and that would create a lot of tension on the brake handle which has no way to support the weight of the chain pulling on it.Mount the coaster to the forks. Get a bike chain,wrap it around the sprocket to a free sprocket welded to your handlebar. Alignment is critical so you need to strengthen your gooseneck so your handlebar won't loosen left or right. Weld a (you all seen this before) "safety lever" used in old school ten speeds with the curled handlebars that connect to your brakes so you can activate it from the top of the handlebar. Weld it to the free sprocket so it sits above your handlebar. To activate,push it down.