Do you have this?
Your shoe looks to be an older version of our 15-241. This may be worth considering, but I am concerned about the stem length. If your balance is particularly old, the 15-241 may not clip into the rivet the right way.
Look it over and see what you think. If this won't work, you need an all new balance.
That hole isn't very important, but length might be. The way these work is they clip on a rivet in the metal channel. I realize now that our 15-241 doesn't list the overall length, which is 1-15/16". As long as yours is the same size then it should work. If not, then it may still work but I'd be less confident.
If the 15-241 isn't a good fit then you're looking at an all new balance. We can cross that bridge if and when we get there, just let us know.
The 15-194 won't work because the stem doesn't have the same groove running down the center as your original, and the 15-241. That means it won't fit in the metal channel. It's otherwise functionally identical, but not worth considering for this application unless you plan on also replacing the channel balance itself.