If you have a digital multimeter you can measure between the posts on the back side of the board and probably get a good idea what the resistance is. That is assuming that it isn't reduced by other components since that is an in circuit measurement. If it is turned where you can see the manufacturer markings on the side then googlefu will get you the value. You also need to make sure and identify the wiper terminal so you can wire the new potentiometer. If googlefu is successful you can track down a data sheet with that info if you don't have a multimeter. The resistance won't vary (or vary little in comparison since this is an in circuit measurement) if measuring across the 2 non wiper posts while adjusting the pot. If one of your leads is on the wiper then it will vary up and down a good percentage of the pots resistance.
I can't tell by the pictures if this is just a 2 layer board (top and bottom traces) or a multi layer (additional layers with traces sandwiched inbetween). If just a 2 layer it wouldn't be too difficult to remove the potentiometer if you have medium or higher soldering skills. If a multilayer or you only have rudimentery soldering skills then I wouldn't attempt to remove it, but rather gently crush it and remove pieces as needed to the point of leaving 3 terminal places to solder wire to. Make sure and not push or pull on it in any direction while destructing it or you could pull traces of the board and brick it. If you don't have some soldering skills you should find someone local that does. Even with the gentle crushing method you could brick it if you apply heat too long.
If this seems overwhelming to you, you probably shouldn't do it. Do you have a local vocational technical school or similar where students would be taking electronics classes? Usually the teacher would allow a student to do this, but if it is bricked then you are just out of luck.
