Spacing is very key to playing the Sheik vs Snake matchup. And by spacing, I mean baiting his incredible range and then using the small gap in time to rush in and punish. This is possible only because Sheik is fast. If he's not giving you those opportunities then hold back, charge/throw needles until he does.
Remember, hitting a grenade with a needle will cause it to explode, hitting Snake with a grenade will cause him to drop it, so if you can somehow time hitting Snake while holding a grenade with multiple needles, the first needle will cause him to drop the nade and the rest will detonate it right next to him. Needles are also good for killing grenades out of the air and setting off Claymores (Snake dsmash). If Snake makes the mistake of recovering low, which frankly he never should, you can try to steal his second jump with needles and force him to recover with the Cypher from under the stage, setting up for the grab gimp.
Ftilt lock is nice, but if you don't have the decay just right then Snake will have enough of a window to pull a grenade and interrupt your lock by blowing both of you up. If you're not confident in avoiding this then just end the lock early with a dsmash or nair.
Since Snake has fast and ranged attacks, you won't want to spam ftilt on his shield (you can actually use this as legit shield pressure when behind certain characters, like G&W). Instead, on a shield hit, either dsmash or go into jabs. Both of those can stuff most responses if you're quick enough about it. If he starts shielding the ftilt into dsmash/jab trap, then mix up a grab.
Snake's aerials are strong and typically out-prioritize yours, but your aerials are clearly faster. Try to bait him into an aerial and then punish the blind spots. If he spotdodges all the better, because that's when you can do empty shorthop baits into usmash (or Vanish if you're feeling silly). Getting him in the air is easy too, through utilt and pretty much all of Sheik's throws.
Snake is vulnerable off-stage and Sheik is good at edgeguarding. For this reason, any Snakes who know the matchup will double-jump Up+B recovery very early to go as high as possible, in order to avoid any edgeguards. In this case just use your usual aerial juggle pressure that I mentioned in the previous paragraph. If he's dumb and/or forced to recover low, go crazy. Bair can deal damage and knock him out of his Cypher armor, fair can force another Cypher, and Sheik has a decent grab range to do the grab gimp.
Snake's midstage neutral game is dangerous. His jabs are as fast as yours but much more damaging, his tilts are quick, and his utilt can KO you at just under 100% when undecayed. His grab game is scary too if you're not used to it, since the dthrow deals 12% and gives an instant wakeup punish setup for him. You typically want to stay out of his range until he whiffs something, and even then you have to move in fast since his tilts and jabs have moderately low cooldown. Sheik has a little trick of crouching under Snake's jabs and being able to dtilt past the range of his grab. Use this to your advantage until he picks up on the gimmick.
Uhh, not really sure what else to say. Ask me if I missed anything.
EDIT: Oh yeah, if you shield ftilt, then shieldgrab after the first hit, but ROLL AWAY if you shielded both hits, because you won't be in range for anything if you shielded both. Trying to punish after the second gets you jab combo'd.