A standard drill press with suitable blocks & clamps is plenty accurate for rechambering a revolver cylinder. You do need the proper size drills and piloted reamers, of course.
The problem in rechambering your revolver from .22 LR to .22 WRM is that the barrel bore, groove, and throat dimensions are not the same for both calibers. The .22 WRM is about 0.0015" larger in groove diameter. This means you are likely to get poor accuracy, or worse, difficult extraction and possible bullet-in-bore obstructions. Convertible caliber revolvers use a compromise bore dimension that works best with .22 WRM, but is safe with .22 LR.
I've seen several rechambered .22LR rifles converted to .22 WRM, and they were all unsatisfactory, including a couple with bulged barrels from firing with obstructed bores.
If your revolver is a quality piece (S&W, Ruger, Colt) I'd highly recommend finding the proper biameter barrel first. Otherwise, this is one of those "not recommended" projects.