Here's my shot at an answer, and further analysis. I hope others answer to, so I can see if my perspective is correct.
You have a few problems to consider, here.
Your aim will be grossly limited. You could try to put a swivel gun on your back, theoretically, and a very flexible centaur might be able to manipulate it. But is such aim even necessary?
Largely, no. Your intention is to charge into a thick line of men, shooting shotguns. As long as the guns are aiming in their general direction, you should surely hit something.
You don't want to kill yourself with a shotgun, inadvertently. So, you need to make sure the shotgun is mounted properly, so that when it goes off, none of the buckshot will hit you.
You might do this with specially long barrels, and by packing filler-material between the shotgun barrel and your body. This will cause the shotgun to point several degrees away from you. This will also prevent a hot metal barrel touching your skin. You might also want to angle the shotgun down, both so it will hit the enemies in the guts, and so it isn't pointing near your arms.
You also need to make sure the guns hang loose-enough towards the butt that you can turn and articulate your horse-body, without the guns restricting your movement. You might need the butt to go across your back, or the shotgun to be towards the front of you (and be short).
You can probably trigger it with something as simple as a fuse or string. Either a matchlock, or a flintlock. You'd need to make sure that during your charge into the enemy, the powder didn't bounce out of the flash-pan.
Once you've fired the shotguns, you may want to loose them. This might be possible by cutting or unbuckling a strap, designed for a quick-release.
It'd take some setup to arrange this. If you have ready-made harnesses with shotguns, and a trained person to fasten the harness onto you, it might be done in a few minutes.
It's had to estimate whether you could have these put on at the last second, before you charge into battle. You might need to wear them for hours, just in case a sudden charge is needed. More than likely.
It seems weird, but it doesn't seem impossible in terms of engineering.
Is it practical? ...Could be. It might not be, due to minutiae, such as being unable to activate the shotguns at the right time. Or even worse, you accidentally set them off and hurt someone. A safety system for the shotguns may be necessary.
If it does work, that's going to be a nice touch. Hitting the enemy with shot-gun blasts as you pour into them. You could even consider the possibilities of using this to try and break into a British Square.
In the end, I'd call it plausible. Worthy of plausible fiction, which explores these difficulties and oddities.