Fine motor skills and finger dexterity matter more for sax.

along with braces, trumpet/cornet can lead to a ring around the lips/mouth which may look like a ringworm. it's basically like chapped lips but you get it around your mouth.

the sax, if you're not grossed out, as with clarinet too, you have to learn how to suck up the spit in the instrument from the mouthpiece.