Wetting a tanned hide should not make the hair slip. If you kept it wet for a long time it may, but just to soften it, it shouldn't. Neatsfoot oil is a good leather softener and can be applied to the leather. You likely do not know if it is a chrome tan or alum tan. A chrome tan will not leach out when it gets wet. An alum tan can and will slowly leach out when it gets wet and will harden after a while. But it should take several times of getting wet.
The face cartilage does not soften easily and you can cause the whiskers to break and fall out, as well as damaging the nose so be gentle around those areas if you try a soften them.
Good Luck..l