Unless things have changed... borders are charging points for train tickets, you would need to buy a ticket to the border rather than the nearest station on the Dutch side. (I used to travel between Germany and the UK on a combination of UK-issued "Any Dutch Station" tickets and German-issued tickets to "Bad Bentheim Grenze")

However, if you know what train you're going to catch, and you are able to book well in advance, then your best bet would be a German-issued "Netherlands Special" from Amsterdam to Oberhausen (the nearest station on the German side) for EUR 19 in second class (in theory there should be a first class equivalent for about EUR 30 - i.e., 1.5 times the second class fare - but the best I could find for the random days I looked at was EUR 49).

Oh, and BTW, there is no country called "Swiss". There are Swiss people, but they live in Switzerland.

PS Having just double-checked... EUR 19 covers you all the way to Cologne, so if you're not planning on taking any other trips on that day you could save a day on your railpass by buying a ticket all the way.