So your trying to splice in a piece of cable that you’ll solder on both ends...one side to the existing USB-C (male) connector and the other back into the 3 wire cable going into the power brick? For sure you’ll have to match up the number and size of each conductor. According to some online literature, we are looking at USB-C Power Delivery (PD). The Red wire is your VCC, the blue is CC (control) and the Black is the Gnd. The CC wire allows for signaling if the voltage needs to change for the sink (load…your laptop, in this case).