I think you nailed the difficulties with a shavette.
Every once in a blue moon I shave with one just because I want to know how to do it, but a true straight is so much better for the reasons you stated.
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Granted, I'm not the most experienced, but it seems to me that starting at a 90 degree angle under the nose would be the cause there. Doing so, as you rotate the blade, you begin to add unnecessary pressure, which will attribute to being cut. Also, unless you happen to be a robot, I would imagine that as you rotate the blade you are slightly pulling or pushing it horizontally in a slight slicing motion, which when combined with the extra pressure will definitely cut you.
Try more of a sweeping motion wherein the blade , starting from a 90 degree angle to get it under your nose, begins rotating before it touches your skin and gets to about a 30 degree angle as it touches your skin, making sort of a "C" with the tip of the blade. See my crude drawing below.
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Like I said, I'm not the most experienced member/str8 shaver, but that would be my guess as to a possible solution (at least under your nose).
its not unique to shavvetes.
after some more practise you wont cut yourself.
go for a shallower angle and try to only move razor in one direction
if you move it side to side you will slice skin off.
this is what most people do rather than wrong angle