Celbii, Hi! and welcome to the Cantina. The fastest way to get a lot of info on this is to do a search of this forum for "rust" or "rust removal." There are probably a few tens of thousands of words on the subject, with different methods to try.
For now, I can tell you that I usually use a green Scotchbrite scrubbing pad soaked in WD-40, or any kind of oil will do. This quickly removes rust and also leaves a satin finish instead of the full polished finish your HI khuk probably came with (unless it's a Villager model or one of Sgt Karka's newer efforts.) The WD-40 leaves behind a trace layer after you wipe the blade down that will help protect the metal against future rusting.
I usually will leave the satin finish as it is easy to maintain, but if you want the full polish back you can always buff it back on a buffer wheel, and trial and error is the key there. I used to use red rouge only, but find that if I start with a slightly more abrasive compound and then work up to the RR that I have better results.
However, if you are going to use your khuk at all for chopping, then I recommend sticking with the satin finish you get with the scotchbrite pad. Every time you use your khuk, you can quickly rub out the marks left by whatever you were chopping, and the khuk will always look nice.
Good luck!
Regards,
Norm