The batteries probably aren't good for crap, but you could put a couple of motorcycle batteries on your belt and run a cable. Half-assed Not An Electrical Person back-of-envelope esticalculations suggest -- I mean, the spirits tell me -- that you ought to be able to get, say, 250 watt-hours.
Now, an extra-powerful handgun cartridge will be around 800 joules, but only very briefly. If you got hit with that bullet continuously for one second, instead of just once for a fraction of a second, that would be 800 watts. That 250 watt-hours would be about 1100 times as much. You're not gonna get great efficiency out of a little diode laser, and in this day and age you're not gonna have a little shocked electron cloud vanishing electron laser, or whatever (do they have quantum cascade lasers yet?), so you want an array of diode lasers, to prevent overheating and such.
Lasers are much more efficient than bullets, anyway -- you can seriously hurt someone with a 2-watt laser, for sure, especially if you use a vibrating quartz optic to make the spot move quickly over the target surface. 24VDC at a few amps input will give you enough output to burn through wood and, pulsed, chew chunks out of concrete. You want near-infrared because it goes through air without power loss. You're not going to get super-long range near full power in a device smaller than the cardboard tube from a roll of paper towels, just because the optic won't be big enough, and you'll get diffraction, but that'll mean a bigger target spot, so it's a tradeoff. In five years, enough money might get you a metamaterial optic, but not yet, I think.
So, anyway, maybe 70 watts, and you've got a handheld laser certainly capable of killing people, even without trick spreading optics. You'd want a regular laser sight, though, with a weaker beam, so you can be sure of your target before you fire. This would be a pulsed weapon, not continuous beam, but it could fire several times a second if you add capacitors. I have no idea what the heat issues would be like. You'd get hundreds of shots before you needed to recharge the batteries, and you could even get several dozen shots using a few D batteries instead . . . .
Military laser sidearms are very possible in the modern age. They're just fragile and not yet as flexible or cheap as standard munitions.