I do what I can with a dry rag. Then use a damp rag to get what the dry rag can't. There's not too much danger of using a water-wet rag or towel on the outside of a steel frame, provided that (a) water doesn't get into the inside of the frame, and (2) the water ou use ain't full of salt, and (3) the area is able to dry off relatively quickly. The inside of a steel frame is a rust-friendly environment. Frames that rust out usually do it from the inside, not the outside.
If you're worried, you can use WD-40 on a rag to get hard-to-clean stuff that a dry rag won't take off. But then you'll need to work to get the WD-40 residue off of the now-otherwise-cleaned area.