What can I do? Nothing. Fire balls stop nades
if you aren't just throwing them straight at him you should be able to get one near him, at that point he has to stop spamming for a moment to deal with it. also try cooking them and throwing them above his spam. beyond that general stage control is key, C4 and grenades should be in constant use, spammers need a safe place to spam from, you aren't going to want to spam when there is C4 or a grenade nearby. also
all of snakes basic attacks will cancel fireballs. of course one thing to be careful with is that a fireball can get underneath jab, it seems to bounce up into it most of the time but better to be safe. so just walk forward and knee, and don't be careless when you get close.
there is also simply outcamping him, get better at getting your grenades through his spam and he's done with camping, while grenades aren't as spammable, you have a huge range advantage, C4 the mid range to make him uncomfortable getting closer and get out of his range
if you do it from the right distance during fireball spam it should be relatively safe, it runs right through fireballs and you can cancel it if mario starts to make a move. he might also instinctively attempt to cape it, cape sends it at odd angles a lot of the time though rather than right back at you, and you can still cancel it, many times it leaves mario open to have the missile dropped on him, be aware of this. if he times it right it will fly right back at you, though, be aware of this also and be ready to protect yourself(if he times it right snake loses control of it and can no longer cancel, just shield it, or you can use the first hit of jab to redirect it away from you safely)