Most any liquid cleaner can be used to remove residue of stropping compounds. Dish soap & water, isopropyl alcohol, Windex (what I use, most of the time), etc. Really doesn't take much to remove it, if the cleaning medium used is wet and/or soapy. 'Stropping' the blade on a microfiber towel moistened with Windex has worked well for me, for example. Alcohol-based gel hand sanitizer could work, I'm sure. But it has no particular cleaning advantage over the other options mentioned. Clean your knives more or less like you'd clean kitchen cutlery (avoid the dishwasher, maybe), and you'll be fine.
Alcohol, by the way, won't create any direct risk of rusting by itself, save for it's tendency to dissolve and wash away any oil that might otherwise protect a non-stainless blade (oil them again after using it). In fact, isopropyl alcohol will bond with water molecules; as the alcohol evaporates, it'll carry moisture (water molecules) away with it. It's an effective way to remove all residual water from knives after washing them, by flushing them out with IPA afterwards.