Can't remember their names, but we used these folks for our black lab. Pretty sure the last name is Winters. 512-263-2416
They offer de-snaking for $60/snake and have Western Diamondbacks, Copperheads and Cottonmouths. We did all three species for $180 and with that comes a free tune-up after six months.
They typically do it on a weekend in the Bee Cave area, several times/year.
We took ours back for the tune-up and she wouldn't get within 30 yards of any of them the second go round.
I'd also recommend you get your dog the rattlesnake vaccine. The vet administers two vaccines, a couple weeks apart. This may not save your dog and it may. The vet says it can cut down on morbidity in dogs that survive snakebite envenomization, by as much as 50%.