Do not try and go toe-to-toe with Snake in a straight-up tilt/jab battle unless you know you have the advantage. Your weak attacks will get beaten out by his (or anybody's) crouch-cancel, and his tilt game packs a wallop. This is especially bad for you if you get nailed with U-tilt, as Sheik's relatively poor aerial movement (both for her tier placement and relative to her superior ground movement) can be a boon to the Snake player. As far as I'm aware, Snake also struggles in that respect, but he has a better SHFFL game all around, so a straight up air-to-air fight might be tough.
The Snake player knows that Sheik loses her advantage once she's in the air for any extended amount of time. Both of you excel on the ground, so try and stay there as much as possible. Snake suffers once in the air, just like you do, so take advantage of that. The battle is going to boil down to who can stay on the ground the longest. Of course, Snake's multitude of projectiles limit your own ground movement, but Snake only gets the most out of them when followed up by his grab-game. Don't forget though, that your grab game is superior, and should be your whole game as Sheik while on-stage. Just play it cool, use your needles to kill his mines, and stay grounded as much as you can. If you do need to get into the air, make sure you've got a reason to; Snake wants to get you up there to needle out his mines, he wants you to get to where you will be your least effective. Don't let him.