I've got two H&K USP Compact pistols. I know, not precisely the same...
But I use any gun oil. I've got some Rem oil, some CLP, I'm not picky, applied IAW the manual directions - a drop on each rail, one on the barrel front, one on the lockup part of the barrel...that's it. Lightly lubricated is how H&K specifies it....
I've not tried grease on the rails.
But, I've put over 4,000 rounds through one of them, and had not one firing issue. Not one FTE, or jam. The pistol functions flawlessly - and that's the most important thing...I'm more interested in reliability than I am in longevity.