I have this problem too! Both TJ and Roxy can get wet paws. TJ when he pees it sometimes goes right to his front paws and Roxy has NO problem walking on the wet spots when she's trying to find 'the right spot' to pee.
I have since covered my whole couch in large blankets and sheets. I strip it down every weekend to wash and re-line
I haven't found a better way to combat this yet