I've used a two wheeler (Hand truck or dolly)at work all the time, and have used those 4 wheel dollies under something. My opinion. (Yes, I know what an opinion is worth.) Get the hand truck. Get a few feet of plumbers tape, and bolt the dolly to the UDS.
I was wheeling an oxy-acetylene rig around Sterling (that guy ^ up there)'s yard, with a hand truck. Because of the LARGE wheels, it was doable. Top heavy, but doable. (We've since put the welding rig on a 4 wheeled wagon, and it is MUCH easier to move.)
Sterling used to have a UDS mounted on a hand truck, and it was VERY EASY to move, even over loose or uneven dirt. Using one of those caster dollies, well, it's going to tip over, or lose the base.
steve