When cleaning toys that have a suede side and a finished side (suede vs top grain), there really isn't a whole lot that has to be worried about as far as altering your cleaning methods because of the suede side. The finished side of the leather actually helps hold the leather together. Imagine having a piece of paper that has been laminated on one side only. That is kind of like what happens when leather is tanned. If you got that piece of paper wet, the lamination will help hold it together.
For a piece of leather that is just suede with no top grain / finished side, you want to try to avoid getting it wet and putting conditioners on it because it doesn't have that layer to help keep it together (similar to a standard piece of paper). For that you want to find a product specifically for cleaning suede. You can find it at most leather craft stores; some shoe stores also carry it. Of course, when all else fails, the internet is another place to find it. Simply look for "suede cleaner."
All that being said, lots of cleaning and roughing up of the suede side of leather will cause it to get "fuzzy" or "fuzzier" depending on the original texture of the piece you're working with. If the ends of your flogger (for example) get a bit frayed and fuzzy looking, simply take some sharp sewing scissors and trim them by 1/8" - 1/4". It will make the tips of the falls feel like new again and potentially add some sting back to your toy. It can also help prevent the fraying and splitting from traveling further up the falls.