Light Socket with one wire

[Yooper421]

The ceiling lamp over the couch has a single wire going to each of the three sockets. One broke off right at the bottom contact of the socket.

I have not been able to locate replacements anywhere, including calling Jayco direct.

I found an exact match on e-bay, size, threads etc., except it has both a black and white wire coming out of it.

Can anyone tell me if I can use that and simply clip the white wire off? I'm assuming that the fixture itself is somehow grounded making both wires from the bulb/socket unnecessary.