Back to the question:
Yes, a solar charger will do the trick - you're only running a little bit of wire, rather than fencing an acre. It needs to be in full sun as much as possible.
No, it won't affect the bees at all. Some/many of us run electric fences to keep bears and other critters out. The fence I'm running is five wires, from 6 inches to 5 feet off the ground (we have black bears, coyotes, bobcats, etc etc) and the hive entrance is only a few feet from it. They sometimes rest on the wire, then go off about their business...
The way these work, if a creature (you, bear, etc) is in contact with the ground *and* a hotwire when the high voltage pulse comes, you get shocked.
If you're not touching the ground (say, an insect) when you touch the wire, there is no effect at all. They send a very short pulse of about 5,000 volts at a very low, controlled current every few seconds, as opposed to power lines, which are hot all the time and will dump a buttload (technical term) of current for as long as the system can supply it. This is what we call a Bad Thing.
I have high tension/high voltage ( half a million volts ) power lines on one side of the property, and when the humidity is right you can get a healthy zap just from touching a vehicle parked under them. Don't know if or how it would affect bees, but I'm betting it wouldn't bee a Good Thing.
Anyway, fence chargers are handy, at least out here. Horses, cows, pigs all have a healthy respect for the wire. Your bees won't even notice that it's there.