Well you could try Maho - that is where the planes fly very low over the beach. No shade there unless you go to Sunset Beach Bar for something to eat and sit under the umbrellas.
Simpson Bay area has swimming. In order to avoid C/O you need to stay on the Dutch side. Also, when you get off the ship or tender there is a swimming area right there.
Lots of stores, etc.
We just returned from a cruise that took us to St Martin in mid Feb. We toured the whole island and spent time on several beaches. If I where going back and wanted what you described I would spend some time at Mullet Bay beach. I has great sand, shade behind and lots of different things to do. Not a watersport rental kind of place, but calm over to the right side for young kids to play. Waves on the left so body boarding. Reef to snorkel on and sand volleyball. It was beautiful the day we went there. As for as nude or topless sunbathers, you may run in to them just about everywhere. Orient beach is the most famous and they where everywhere on that beach, but we did we alittle bit on all beaches.