You definitely do not have to worry about anything closing down as early as September. Hotels, (beach)restaurants, etc etc will all remain open until at least the end of October, with many staying open all year round.
Also, the North Sea is perfectly safe to swim in and in early September the water temperature of the North Sea has only just reached its peak temperature, so you can still swim in the sea. The English Channel and the Atlantic Ocean are located elsewhere, so I’m not sure how their temperature or safety is relevant to this question.
If you depend on public transport, Zandvoort is probably the easiest beach town to reach from Amsterdam but it isn’t the nicest one.
I personally like Noordwijk a lot, but it’s more difficult to reach by public transport. Scheveningen is another good option.
For something completely different, check out the island of Texel. It’s one of the 5 Wadden Islands and well worth a visit.