When I was using compounded strops, I cleaned them with either WD-40 or isopropyl alcohol. I'd suggest, if doing so, it's better to apply the solvent to a microfiber towel and wipe the leather with that. Don't get the leather too wet with it. I had one experience getting the leather too moist with WD-40. Some of it leeched through the leather and loosened the adhesive bond to the block underneath the leather. The leather started peeling away from the block. This happened with a strop block I'd made myself.
And for sanding, I found that garnet sandpaper at coarse grit, like 100 grit or so, works very well. It's the type of sandpaper generally recommended for wood. There's little risk for contamination this way - the grit is large enough that if some of it comes off the paper, it won't embed in the leather and can simply be brushed off. Wrap the sandpaper around a wooden block and use a light touch for sanding - nothing heavy at all. If you feel you need to, use a vacuum cleaner to follow the sanding. In my experience, I seldom needed to do that, as the grit from the sandpaper never created any issues on the leather. Sanding will leave the surface of the leather with a velvety nap at first. But after application of compound and a little use, the nap on the leather surface will smooth out. This is a very easy and effective way to thoroughly clean a strop. It works very well.
Avoid using silicon carbide wet/dry sandpaper on leather. The grit is more friable, and the paper will shed SiC dust, which is much more likely to embed and contaminate the leather.
