as NK cells do not differ e.g. in density from lymphocytes there is no other way than separating them from other PBMC populations with the use of antibodies.
Magnetic-bead coupled separation can be done with dynabeads, stem cell technology, MACS. You always need a magnet which you cannot access (but if you plan on working alot with blood populations you should think about getting one).
There is one magnet-free option: Rosette-Sep from Stem cell technology. Unwanted cells are "linked" to red blood cells. Then you do your normal density gradient step and as unwanted cells sit at the bottom of the tube together with the red blood cells, the interphase layer only consists of your cells of interest. You'll find the product via google. I think it is more pricy than doing it with a magnet but compare yourself.
Alternatively, fluorochrome-coupled antibodies can be used for cell sorting but you stated that you do not have any access.
Prior to the development of antibody-based purification, nylon wool non-adherent splenocytes were used. Have a look at Hidore MR, et al Infect Immun. 1986 Feb;51(2):547-55.