Not dealing with her mouth is more dangerous.
If you want to show and it's holding you back, than get it done. Her age is not a problem. If she flips over on you from the pain, that's a problem. Normally, she would get a general and a little local and they'll just pop the tooth out with a pair of pliers. It will bleed and look worst than it is. Jointed bits will tend to "break" and rest on the bars, in her case bumping on the tooth thus causing pain, so going with a solid mouthpiece is one place to start. The shape of the mouth, tongue, bars plus your hands are going to be part of the selection process. You're just going to have to experiment. Hopefully you have friends with all sorts of different mouthpieces because if you have to buy to try, it gets expensive rather quickly.
I would find an equine dentist who is better versed with dental issues than your regular vet.