You can use inflatable arm cuffs at the resort pools, but they are NOT allowed at the water parks. The water parks require the use of vests. Both the resorts and the waterparks will supply vests at no charge.
One more point: so-called "swimmies" are actually pretty dangerous gadgets. It is very easy for them to slip off and/or deflate if accidentally nicked, and they impede the movement of the child's arms. It is really MUCH safer to use a properly-sized vest for recreational pool use. ("Swimmies" should NEVER be used in open water.) For a child under 3, the vest should have a crotch strap and a float collar that will keep the child's head above water at all times.
If you use a boat-float seat for an infant, you hand should be on it at all times. (And it isn't a bad idea to have a vest on the child, too, if you can find one small enough.) For babies, you can also use a water sling in shallow water.