Snake is kind of an interesting case, simply because he can keep you at range without using standard projectiles or kill you in melee without using smashes. The thing is, that's how he HAS to play.
I generally engage him at medium range. Tip him with with forward smashes and fish for Paralyzer hits. The thing is, Snake has some Excellent tilts, but his f-smash is garbage and d-smash, while useful, is not for straight up combat. U-smash is awesome, so don't approach him from the air. If he breaks away from you, short hop paralyzer after him. You're in trouble if he tries to close, because he beats Zamus in close combat, but if you can tag him with a d-tilt, you can hit him with a long and very powerful combo. From there, just keep the pressure on from a safe distance and don't let him set up a wall keeping you out.
Snake can knock you around, but if you don't let him launch you straight up or into a planted bomb, he actually has a hard time KOing. He's not a great edgeguard against someone like Zamus, who can tether and avoid bombs. Pin him down and keep him pinned down.