Can नहीं not be moved to before हैं ? (It isn't accepted.) i.e. if literally translated 'it is not that we are swimming today' rather than 'it is that we are not swimming today'.
No. The two possible placements of नहीं are before तैर and after तैर (ie, before रहे).
But note that the nuances that your two English sentences communicate by differing placements of 'not' don't come across in Hindi by changing the placement of नहीं.