Moet peds w/o batteries use ac power for the lights. The lights don't care but a battery sure as hell would.
You can do this, and given the relatively low output of a ped's alternator, you most likely do not need a regulator. The alternator will not burn out, my Motobecane shorts mine to ground when not being used.
Find a book on simple charging circuits and a reasonable VOM and learn how to use it before you start.