Definitely not on Happy Bay Beach. That beach would be B.Y.O.B. If you go there, bring beach towels and a portable beach umbrella, also. I don't believe you'll have that kind of service on Cupecoy, either. I'll let others try to answer that for you because it's been a few years since I've been out that way on the dutch side.
Orient Beach, however is a much different story. If you intend to go nude, you will head for the southern end of the beach which is totally clothing-optional. You can rent chairs and a fixed beach umbrella, but the chairs are not as nice nor as fully padded as those on the adjacent primary beach. But, if you throw your towels over them they're okay and I've sat on much worse in the past. For food or drinks you'll have to get up and take a short walk over the Perch Bar & Grill which is run by a man named Cedrick and his staff. You can do this without the need to put your suits back on if you so choose, because this bar/restaurant is also C/O. The day my wife and I were there the number of people eating and drinking - with or without apparel - was roughly 50-50. There is no chair service for ordering drinks on this part of the beach (at least I didn't see any the entire day we were there).
If you decide that chair service is something you prefer, then stick to the three primary beach bars to the north: Kontiki, Bikini Beach, and Kakao. All three feature staff that comes around from time-to-time to see if you need a drink or wish to order some food. But, full nudity is prohibited on the main beach though many women choose to lay out top free and do while ordering food and drinks throughout the day. The one day we visited Bikini Beach the young couple right next to us chose that approach. A good compromise for doing both is to visit the C/O beach in the morning while soaking up the sun, grab lunch at the Perch, the head over to Kontiki which is close by. If chairs are still available lay out there in the afternoon while enjoying 'chair service' on the beach and your favorite drinks. However, you'll be renting beach chairs twice in the same day with that approach. Hope this helps.