Our two new Blue Siamese cats (nowadays called Thai cats) are adjusting to our Catalina 309. Our previous cat was all trained in on our vessel, but passed away last winter.
The new cats, Kit and Boo, were introduced to the boat gradually and are doing great. They both tolerate the dinghy, but Boo, the boy, will actually hop in it and talk me into taking him for a ride.
I wrapped the leg that supports our dining table with sisal line, so it's a scratching post.
The litter box is a big, store-bought, covered type, with a translucent lid so they don't feel confined. I used Velcro to attach a collapsible cat tunnel to the opening of the closed box. This eliminates litter tracking by more than 90 per cent. I just made sure they got to play with the tunnel at home before it went on the boat, so they have a positive attitude about it.
Heavy sailing/heeling will make them puke, but otherwise they do well. They quickly found the best napping spots, and prefer the v-berth while underway.
We don't daysail with them, but we wouldn't go on a trip without them. They're leash trained and love to wander around the marina, etc. with us.
I guess the key is to go gradually, and make sure they have everything they need on their first visit to the boat: food, water, cat toy, scratching post, and litter box. Particularly the litter box, as it puts them at ease. They quickly learn that the boat is their vacation home.
Lastly, to each their own, but when underway they are either closed in the cabin or on their tethers.