This isn't a good idea unless you are able to buy a live mouse every week or care for a bunch over time. You probably will not be able to get him back to f/t easily once he's eaten live. If you decide to feed live there is nothing wrong with that, of course; personally I find f/t is less expensive and more convenient.
Seems like either you've got a picky eater (it happens), or the snake is not feeling secure in his enclosure. If he is constantly roaming around it sometimes means he does not feel secure. What does his enclosure look like?
Also, was this snake eating f/t mice well with whoever you bought him from?