Backup Camera Wiring Question

Just realized I should have asked this here.

Had to replace the tailgate handle because it was broken and I had a camera in it. The new handle has a new camera and I am hoping to not have to run new wires all the way to the radio. Directly to the old camera I have a red, black, white and yellow wire and I am wondering if I can connect my new camera's connector (the one that would run all the way to the radio) to the old wiring and then plug into the new camera. The new connector has a red, white, black, and dark gray wire. I am not an electrical genius but I am comfortable splicing wires or replacing things when they are exact. When they don't match and I need to use a volt meter is when things go bad. The new camera is from Master Tailgaters.

Anyone know if I would be able to do this or do I just need to run the new wire all the way to the radio. Hopefully this makes sense.