Well, there are a few things you can try. First off, I would suggest you try to bait him into using the tilts at the wrong times (Like for example coming from above, do a jump right before you get into Utilt range, and if he Utilts, go to stone (providing you can transform before his Utilt ends... haven't tried it, so I couldn't say, but I think that one would work.), or baiting him into using an Ftilt the same way, only with short hops, and either eat him or hammer him.).
Also, since it sounds like he isn't using grenades, Nikita, mines, mortar slide, etc, you have the whole level to yourself. Use it. Stay out of his range while trying to make him mess up, and punish him when he does. Also, if your on a level with platforms, Uair him through the platform.
Another thing you could do is final cutter edge grabs. What I mean is do Final Cutter from a ledge (it goes through the stage on the way up and back down, but doesn't shoot if you don't land on the ground.). This should dissuade him from staying too close to the ledge, and, on top of that, it makes him never know when to expect the shockwave or not, allowing it to usually hit when you do randomly land on stage.
Finally, your B move will be your best friend here. When you start sucking in your opponent, you get super armor frames, meaning you can eat him through his Ftilt (providing you space it correctly). At this point, you can try to spit him out (into a mine if he laid one) and chase, Kirbycide, or take his grenades. All will help a lot against Snake.
If you take his grenades, they can be a HUGE help. Pull the out and shield/roll away from his tilts to make him blow himself up on the grenade you left behind. Otherwise, use them the same way a Snake would. Let them stew, then throw.
Grabbing can also be a huge help here. If you know he's going to tilt, shield grab him. From there you can follow up with some impressive combos.
I would also suggest a running Usmash, but I don't know if it outprioritizes Snakes tilts or not.
Hope that helps.
