As for Shadow using guns in Smash, I do like the idea of it being something he could take out during a battle with limited ammo, but making it flow well is another story. It could maybe be part of his Final Smash(even if it's just throwing it away cause he doesn't need it) or his victory screens. Even Sonic 3 goes in with this factor. He'll use whatever it takes to win.
That said, in his own game, he actually cannot use his Chaos Powers in the story till he gets a Chaos Emerald. He lost his memories, and that's part of what outright reawakens them. It's just him using what is a method that simply is available and works to get through the areas. Besides that, it might seem odd his physical attacks are weaker, but he can't really apply his true power of he doesn't remember how to use it correctly.
It's not really a great way they went about it, or even a good excuse. It's just a silly gameplay mechanic(which actually is pretty fun to use). But the justifications are decent enough as an excuse plot in itself. The actual game plot is a lot better, though(albeit, the multiple story options make it a lot weirder, but there does seem to be somewhat of a fairly canon-like route).