I don't know about how the potassium would affect the effectiveness of the AR mix, but either will form the HNO3 required plus a salt that stays in solution (NaCl or KCl).
I would assume that as long as you adjust the ratios of the salt in your formula to account for the difference in atomic weights of potassium vs sodium you would be okay.
Both substances contain the same molecule you want 'NO3', you can actually make Nitric Acid out of either salt. Here is a quick how to (this is a VERY DANGEROUS ACID, It will stain your skin, eat your flesh, burn your eyes, and it's vapors can kill you two weeks after you breath them !!!) BE CAREFUL, BE SAFE, DON'T BE CARELESS OR STUPID! I'M NOT RESPONSIBLE if you bring about your own SELF DESTRUCTION!:
Mix two parts of the salt (Na or K Nitrate) to 1 part H2SO4 conc (Sulfuric Acid- Main line septic line cleaner from hardware store) and distill (all glass rig) the HNO3 out of the mix. You can get 60-70% HNO3 this way if you keep the still head temperature at 83 C and the receiving flask on ice.
There is even a 'speed method' where you mix the above chems, let sit overnight, filter out the solids and use as is. I've never tried this one so I can't vouch for it.
Personally I use the lab grade 70% stuff when I need HNO3.
Steve