After you gently dry burned (i.e., to remove the gunking) your Ni80 coils by letting them glow red-orange and letting them cool down after, you could rinse them with tap water (or mildly sparkling water, which is what I use), and, repeat these steps a few times before doing a final rinse with tap water and letting them dry again. However, I find that after the Ni80 coils have dried, gently pulsing them again and then letting them cool down again before I insert the fresh wicks is all it basically takes to completely get rid of any metallic aftertaste.
I use only premium quality Ni80 wire that's smelted by Sandvik (the same company that owns the official "Kanthal" brand name, which isn't Ni80 of course, but they also do make the best Ni80 wire) in Sweden. Examples of brands that make regular sized spools of premium qualiy wire and that use reliable spooling techniques intended specifically for coil builders are Twisted Messes in the U.S. and wireworks.eu in Europe.