If the frame material is steel, you can cold set the frame. However, that is a one-time operation, you can't reasonably cold set it every time you decide whether to install a 120mm OLD or 130mm OLD wheel.
If the difference between two OLDs is small enough, it may be realistic to cold set it to their average, such as 132.5mm allowing both 130mm and 135mm wheels. However, 120mm and 130mm have such a big difference that it's not realistic to cold set to 125mm to allow choosing between 120mm and 130mm.
I recommend targeting 130mm. 135mm would allow a better durability wheel, but jumping from 120mm to 135mm is riskier than jumping from 120mm to 130mm. It shouldn't be hard to find a 130mm OLD hub.
Note a multi-speed bicycle requires a derailleur hanger (and ideally cable stops too but you can run whole length housing and zip tie the housing on the frame). If you don't have the hanger, you have to devise some kind of a solution.