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Replace the guide rod spring configuration with some sort of Hydraulic or pneumatic plunger? Lol.. I dunno if those even exist, or if I just made it up

Is the spring tight around the guide rod? I know that on 1911's, there's quite a bit of room between the guide rod and the spring. It is not constantly rubbing on it all around.

I've never had a USP apart in front of me, so I don't know, but maybe you can put a larger diameter spring on there that doesn't ride the guide rod as tight?
This starts getting into the 'expert on USP' territory, of which I know nothing about, so I guess my suggestions end here :) Good luck, and if you DO figure something out, post it here for all to see!

Thats just it. The spring and the guide rod are so smooth, they only barely rub, creating your squeak. As they wear more, it will stop. About the only thing you can probably do is just shoot it a lot to wear it in. Either that or maybe hit your guide rod with 1000 grit where it's rubbing to make the squeak, roughening it up ever so slightly. This is probably a really bad idea though, and I wouldn't do it. It also will not guarantee it goes away.

Is it a coated spring of some kind? plastic/rubber/something on it, other then just bare metal? You didn't specify what kind of handgun it was. I don't even know if any handguns do have coated springs, but I know they exist in other things, and something like that could easily cause a squeak.