Yet his starring role, that he is best known for, he uses guns. It's safe for everyone to admit at this point, when they think Shadow the Hedgehog, they think guns. It would simply be unfaithful to make him playable without his iconic pump-action machine gun.
Another issue is that Shadow is well known to use foul language, so they may have to tone him down a bit for Smash. It begs the question though, is it really Shadow if he can't say "Damn!"?
I still think Shadow's most well known appearance is Sonic Adventure 2, where he premiered. And arguably, not even the DC original version, but the GCN port. Maybe that's because I've never played Shadow's game, though. SA2 was the first Sonic game on a Nintendo console. It was a huge deal, and being a launch title on the GCN certainly didn't hurt, either. It was all over Nintendo Power, all over the Internet. Future Sonic games would continue to heavily reference SA2, and future Sonic ports and games would implement SA2:Battle features into them (like SA:DX). For Shadow's boss fight in Generations, it was SA2 that was what they went with, not Shadow the Hedgehog.
That was the game that cemented Shadow in people's minds as a popular character. Shadow (the game) was created because Shadow was already iconic and very popular.
And Shadow hasn't used guns or swore in almost 15 years, and yet the character keeps being used and remains very popular. I don't really think it's as much a part of the character as you think.