I like the idea of running no battery, personally I'd use a 10,000uF (thats micro-farad) capacitor in the place of the battery. Exactly the same connections, just a solid state device thats relatively light and small.
Alternatively you could run a small battery. It'll be easier to find, possibly cheaper as well. I'd recommend anything you can find between 1.2Ah and 3Ah - these sizes are small and can be had in sealed units. The 3Ah is generally a lead-acid style, I've run one in my RS125 with full road lighting and electronic start and have had no problems in several thousand miles since fitting. It'll give you a bit of leeway if you have some sort of charging problem, although it is significantly larger than the 1.2Ah sealed unit, which is around 2/3 the size of a chunky mobile phone.
Cheers - boingk