In my experience with human primary NK cells, they are not attached to the well plate the same as adherent cells, therefore there is no need to trypsinize the cells. I hope it helps you.
Being lymphocytes they ought to be in suspension (not adhered). Check the flask (plate or wherever you seed them) on an inverted microscope to make sure the are in suspension. By the way, if you are changing culture medium you will have to pellet your cells (by centrifugation) before doing it, that way you will avoid losing the cells along with worn off medium.
If cells are loosely "attached", they can be detached (dislodged) by stroking the plate. If cells are tightly attached, check for NK cell marker to make sure that they are the "NK" cells. It is likely that "attached" cells are not pure NK cells.
Trypsinization is not needed. You can rock your culture plate or flask gently and then collect all media, After that, centrifuge the media to get NK pellets. If you still doubt, you can stain with murine NK markers to validate it by flow cytometry