Shadow plus guns = meh/seriously?
Donkey Kong plus guns = what the **** were you smoking?!
Shadow is from a series where modern (and even futuristic) weapons are a thing.
Donkey Kong is from a series where the closest thing to a modern weapon is a blunderbuss that shoots cannonballs, barrels, puffs of smoke, and even has a vacuum feature. And that's from the villain.
Shadow is a rather dark individual that will stop at nothing to achieve his goals. While using firearms wouldn't be out of character (unlike if say, Sonic used them), the main thing that's jarring about that is that Shadow is the Ultimate Life Form and has the power of Chaos Control and its many variants. Why the Hell would he need something as pointless as a gun?
Donkey Kong is an oafish ape of brute force and temperament that loves bananas. How all that translates to "using a double-barreled shotgun" is beyond me. It makes less sense than Shadow using a gun, because at least Shadow would know what a DAMN gun is and it wouldn't be out of character for him to use one.
DK would be more likely to stare blankly at the shotgun, mess with it since he has no idea what it is, and accidentally blow off his foot or blow his brains out. Jungle technology makes more sense for someone as primitive as DK.