if that is indeed a Uniglide freehub under there you may be able to remove the cogs with only one chainwhip if you do it with the wheel in the dropouts and use the crank and chain as one whip.

as far as tools go, yes TWO chainwhips would be better and a couple of cone wrenches for the, what else?, cones. i don't know what size they may be, although i have one of those front hubs, so i would take measurements of the flats before purchasing or go the the LBS with both wheels in hand and throw yourself on their mercy and ask them what you need.