Just about any 1/4"- 3/8" rope would be enough to lower a 200# filing cabinet down a flight of stairs. With a 37-40 degree stair angle and frictional resistance, there will be very little actual weight on the rope, probably under a hundred pounds. (unless you let it go and it builds up a head of steam before it takes up the slack...) It's just not that much of a load.
In fact, you could probably braid something suitable out of pocket lint and the hair from your shower drain....
Put it on a stair dolly and forget about the rope; it's just going to be in the way of the dolly anyway.