Well, the good news is that it works. :) Mounted to a south-facing fence, the battery stays charged very well, varying between 3.2V in the morning and 3.4V in the sun:
I've now moved it to a north-facing fence post. That will be a much more interesting test. :)
The bad news is that the beeper is currently completely pathetic. It's as "loud" as a digital watch. :) No way a blind person can locate it by a busy street! I'll need to work on a different option for that.