The truth is the ignition systems were designed for use with a battery. We prefer AGM (absorbent glass mat) type. The bikes will not work with a capacitor (or battery-less) system nor are they a magneto system (commonly found on dirt bikes, and lawn equipment).
We get a number of questions regarding the use of Lithium ion batteries in the old Honda twins due to their small physical size. Li-ion batteries are generally more sensitive to charging voltages, which are not as accurate from the bike's primitive charging system. For this reason we do not recommend the be used for these specific bikes. If you do choose to try a Li-ion battery, make sure to test the charging voltage range on your bike and consult the battery manufacturer to ensure your bike does not exceed their specs.
The regulator/rectifier combo unit we offer is not MOSFET, in case that is a requirement for a specific battery you may want to use.
If you really want to go smaller, the closest, working, approach we've found is getting a physically smaller SLA battery, generally used on alarm systems, etc. It can be fastened up under the seat where it's out of sight. Anything over 5 Ah should work.