I guess I'm missing something here. Are you married to the idea of an electric shaver? If so, Norelco makes a really small one for about $10-15 that operates on either AA or AAA batteries (I don't remember). They don't last long and the replacement blades are twice as much as the whole shaver costs.

Otherwise, I remember seeing a shaving tool for bald men that fit on the finger like a ring. It was really tiny and I thought about carrying one with me for my face when I was traveling for business. That idea never materialized, though, so I don't know how well this shaver would work for facial hair. Below/attached is a pic:



I'm not really sure why shaving tools would be such a big problem for a cyclist. The shaving CREAM is probably the heaviest component, and you can eliminate that by using ordinary facial soap or, better yet, shaving soap, which will foam up to a really nice lather. Then just grab the razor from your bathroom and throw it in a bag so you have something you know will work.