If the motion of the blade is perpendicular to the edge of the blade, it shouldn't cut you no matter what angle you hold it at (some angles will cut your hair properly but none should cut your skin.) If the motion of the blade is parallel to the edge of the blade, then you're going to cut yourself.

It's not like other people have armored skin that's immune to sharp things; we all cut just as easily as you do. It's a matter of technique.