I've been using those disposable alcohol pads (like the Dr uses before giving a shot) and give a quick wipe and it's working good for me.
The fact that folks dry burn or torch Kanthal A1 or Nichrome will generally burn off the residual oils from manufacturing, while Ni200 normally is not dry burned, so cleaning is a must.
One thing I've noticed, and others have as well, is that some of the "taste" that is noticed even after cleaning is actually a LACK OF coloration of the taste by the wire. Kanthal A1 (yes, I'm particular enough to specify A1 when mentioning Kanthal, as Kanthal is also the manufacturer of the NiCr that I use) alloy has aluminum, iron and chromium in it. The chromium and aluminum don't add any flavor, however iron has a distinct flavor. Likewise, the aluminum and iron will oxidize very fast (this oxidation is what makes contact coils actually work)-- and these oxides DO impart a flavor.... So some or most of the flavor difference between the wire types (barring residual machining oils) is due to coloration on the Kanthal A1 side. This is NOT saying that A1 tastes better or worse than Ni200 (or NiCr), but validates that there IS a difference.
Now thats an informative constructive post!

One step further..... Walk in to any of the top 5 restaurants in your town. Are they using Stainless Steel cookware ( Chromium and Nickel) or Cast Iron? There's a reason the top chefs in the world only use cast-iron.