Anything that ends in "ology" is Greek. I happen to have studied a pretty fair amount of ancient Greek in college. So let me give it a shot:
How about the Greek word temno? Cut, wound, castrate, cut up, cut off, prune, slaughter, chop, hew, quarry, plow, or sever. Temnology: study of cutting. Good, but not really it. A lot of folks here aren't into all the minutiae of cutting things, they just like knives.
Let's try machaira. LSJ gives "large knife or dirk, carving knive, sacrificial knife, short sword, dagger, shears or scissors, blade." I have to admit I don't know for sure whether that yields you machairalogy or machairology. Either way... better, I think, than the above. Captures what we're really after here. Doing an Ology of bladed things, from machetes to edged jewelry.
With that said, I'd like to submit to the group machairology. (muck-EYE-rology) The study of knives.