Scheermes kind of sounds like shear which helps me remember. Shearing is when you cut wool off of a sheep; you shave it. :)
In Dutch there's only one word for shearing and shaving and that's scheren. The knife used for this is a mes for scheren, so a scheermes. :)
I don't even know why we have a specific words to describe the shaving of a sheep! I suppose it just pertains to shaving animals with wool type fur in general.
It's to do with how each one is performed.
To shear can also refer to other types of cutting (e.g. with a sword) and is cognate with the Dutch scheren. Traditionally sheep were sheared using what was basically a pair of scissors, i.e. the blades cut through the hairs but didn't really contact the skin.
To shave originally meant to scrape off, and can still be used like that (e.g. shaving wood). It is cognate with the Dutch schaven, to plane, to grate etc. Think of how a cut-throat razor is used: you're basically scraping the hairs off.
These days with electric razors/shears the line between the two actions is blurrier, but historically they were separate actions.
Incidentally, I believe some Jewish sects forbid their followers from shaving their beards, but cutting with scissors is permitted. By extension they are allowed to use electric razors, since the action is the same (they're basically tiny electric scissors).