Best case scenario would be to de-solder that pot and solder in jumper wires to your new pot, but since Im sure you dont want to take a chance of screwing up that board, you can try just connecting the new pot to those solder pads.
Then you can leave the old pot turned to midway position.
To find out what connections are what, use an ohm meter (DVM is best), turn old pot all the way down (silent).
measure between two of the solder pads. The two reading the lowest resistance (very close to zero) will be the ground and the wiper.
Now turn the pot all the way up (loud). The two measuring the lowest resistance will be the wiper and the input.
By process of elimination, pick out the wiper. That will be center tap on the new pot.
If the new pot acts reverse (up is silent, down is loud), just swap the two outside taps on the new pot.
Your modification will work a lot better if you just remove the old pot though.