I have an older laptop PC. It has a inline transformer. In other words,
the transformer is between the wall plug and the PC. The little plug
came off where it plugs into the PC. I have some of those plugs, but
there is not enough wire between a cord choke, that is right at the end
of the cord by the PC. It's molded on the wire so I cant move it.

What would happen if I just remove it and put my plug on without that
choke? What are those chokes for anyhow? I can understand them on video
cords and so on, but why are they needed on a power cord?

If I can install my plug without the choke, I will, and that will only
be for a short time. I bought a new cord on ebay, but I use that
computer all the time and dont want to wait till I get the ebay one.
After that, the repaired one will only be a backup cord.