Back when I had cats, I used to push them into the bottom of the bathtub by grabbing them by the neck behind their ears. That fairly well immobilized their weaponry.
As to dogs getting sprayed by a skunk? The dog getting sprayed when you're on a camping trip. Tomato juice is what I used to us to deodorize the dogs. But our dogs were outside dogs so the process didn't have to be perfect.
The funniest encounter that I experienced happened with an Australian Shepherd. He had his den under the kitchen porch and he liked to collect things and bring them into his den. One evening, I suddenly detected the unmistakable odor of skunk. Now when you live in the country, you learn not to go charging out of the house when there is a strong smell of skunk.
I cautiously opened the door and scanned the vicinity. No wood kittys in sight. So I got a flashlight and stepped out to see if I could locate the source of the odor. It didn't take long to find it. The Aussie had a young skunk cornered in his den. The skunk was too frightened to try to push past the Aussie and the Aussie wasn't brave enough (or maybe dumb enough) to charge in after it. A Mexican standoff.
I tied the dog up some distance away but the skunk still wasn't budging. I went around the back off the house a collected the garden hose.and starting wetting down the skunk. Every time it turned its backside to me I hit it with a broadside in its little pink rear end. Eventually, it took the hunt and decided to make a run for it.
All that water helped to knock the scent down but it was several days before the atmosphere around the house was tolerable.