Hey there, I'm pretty sure that you have to run a battery on these old honda twins. I'm working on a '74 CL360 and I know that a battery is required for this particular bike. From what I know the electrical sytem is not exactly robust. I think your best bet is to get a smaller battery that will give you enough juice, try a dry cell or gel battery. There are some pretty small sizes, then just get creative with where you mount it. Hope this helps you out, maybe some one else has a definitive answer for you.
Catch you on the flipside,