Hi inman, and welcome to cruise-chat.
We cruised with our son when he was in both the car seat and booster seat stages. We always brought the seat with us. When he was under 2, we used the car seat on the plane, but as booster seats are not FAA approved, you will have to check those. You can check them with your luggage, or at the gate. Of course, the latter means you'd also have to lug the seats around in the airport, but perhaps the kids can help with that.
Once on the ship, you can store them under the beds. If space becomes an issue, ask your cabin steward for assistance. (BTW, are you in one cabin or two?)
I always say that safety doesn't take a vacation. If it were me, I'd take the booster seats, just as I would on any car ride.