ReShade alters the entire image. So we could make your entire screen black like your khajiit's fur... but you won't be able to see anything else.
Unfortunately, I don't believe anything can be done except these few options:
1. Don't be a vampire, or
2. Obtain or buy a skin to use.
Until ZOS hears us after years and years of pleading, we're stuck with the current vampire look. I don't like it either. I'd rather use a rotting skin that I have than look like a vampire... but I like a passive or two from the vampire line.
If anyone else knows of a way, or is willing to attempt to create a way, to revert the look of vampirism... please let us know.