No - you don't need a ticket. My Dad and I did the water shuttle over to the Arizona Memorial without tickets, for only the cost of a TheBus pass ($9 each). We set out at about 11 am, on the #20 TheBus, and got to the Park around 12:30. We had our pack lunch, and then due to a lack of planning ahead, my mom waited outside with our backpacks, because we weren't gonna pay $7 per bag at the bag check. If you have a clear plastic bag, you can take that in, but nothing else, not even a small purse or camera pouch. But we saw the museum, and the movie, and paid our respects on the Memorial. The water shuttle leaves every 15 minutes, and carries a pretty big group. On busier days (we were there mid January, not busy at all), you may need to wait a bit longer than we did (10 minutes or so) but I don't think you will be shut out completely if you don't have them. That said, reservations are helpful if you can get them. While TheBus drops you off in front of the park, you have to go out to the main road and off to your left to get TheBus back to Waikiki.
I also recommend Roberts Hawaii - they are in charge of doing the optional motorcoach transportation up to The Polynesian Cultural centre, and our driver was very talkative, pointing out various landmarks, telling fun stories, and so forth.