Firefly, you need to grab Snake more and be more grabby at the edge.
At the edge against Snake, you only want to attack when they're a ways off the stage and mostly horizontal with it. If they're recovering low, don't attack and grab instead (or edgehog if they will sweetspot). If they're recovering high, just sit back and grab wherever they land. Don't go for A attacks or eggs when they're so close to the stage; just wait it out, find out the scenario they're putting themselves in, and then use the appropriate action. At first it'll seem like, "No way this will work if I do it over and over," but this is less of a mindgame and more of a technique.
It's like rock-paper-scissors except this version is rock-index card-pocket knife-boulder because there is seriously nothing Snake can do when he's in the positions you were able to get Snake into in your matches besides rely on luck or error on your part, but you tried to capitalize in different ways; stick to a really really gay and basic strategy when you get Snake in that position and you'll end up doing much better.
Like in one match, you grabbed Snake and did a down throw and then waited him out and grabbed him as he landed. Another time, Snake was falling from a cypher onto the stage and you just waited it out and then upsmashed for the KO because he couldn't do anything about it. Do that, except all the time when you get Snake to the edge.
Remember, either:
1] Force him to attempt a sweetspot and edgehog,
2] Force a low recovery and grab the cypher, or
3] Wait out a high recovery and throw off the stage to repeat.
This is one of the few win-win, or rather, win-can't lose, situations for Yoshi in this game, so milk all you can out of it.