Bypassing the circuit board of string lights
Am just a beginner but I think the best way to start your plan is to measure the voltage output of adaptor with the LEDs switched off or disconnected. After you measure that check the input of your LEDs, if there is no label then you can check them one by one using a cellphone charger or 5v dc adaptor. Use the positive and negative wire to determine how much brightness it can produce with 5v dc, and it can also determine if that LED is working. And also 5v is not that powerful enough to overload the current through led so I think it is safe. After you measure/check every LEDs, you can sum them up (5 LEDs = 10DCV) then start a way of using components to make a suitable power output for your LEDs, but I suggest to you is just buy an adaptor(laptop adaptor) with at least 24v (to power up all your LEDs).