How can I shorten the length of the light cord on a Hampton Bay track system ?

There is a tube that plugs into the track that has a serries of screws but there is also a screw at the light base also.

Don't know about that model. Would take one apart, you will know if you can.
Various strain reliefs, and they need to continue working after modification.
Leave no sharp edges or burrs.

I have the same. Take the base off the track and unscrew the bottom. (No screws, it is the plastic piece that unscrews) Pull out the wire and there is a white plastic stop the wire runs through. There is a piece with a arrow pointing up to open, open it. Your wire will come loose and you can adjust the length. You may need to cut the wire above the plastic piece because there is little room for excess wiring. Strip the wire ends, remove the orange wire nuts and twist the new end to the transformer wires and replace the nuts, the white plastic stop and screw the bottom back on. You should be OK.