In Oblivion it is called and referenced as the "ring of Khajiiti", which is the correct plural form of Khajiit. Not Khajiits. Since Oblivion is considered canon I would suggest altering this.
You could probably use a one of the spells to make the ring make you seem invisible, I dont remember if there are spells actually saying they make you invisible but the shout spells include one that makes you a ghost, which would make it feel accurate, I believe its "become ethereal" however, this may require some scripting that would use SKSE, and you'd probably want to give that work to someone very proficient in it, like TrainWiz or a few others who've made names for themselves as it would be a simple job quick job for them compared to what they normally do, regardless its great that you added this in, I hope someone makes a good quest mod using it so it'll feel like a proper champion's artifact ^^
This mod seemed to work just fine until I installed Rings of Power, now even though the mod is installed and loose files is checked, I can't find the ring in the crafting list anywhere.
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https://www.nexusmods.com/skyrim/mods/42564
It is a fraud
Calixto...?
EDIT: I fixed it by going editing the ring and adding DefaultRace to applicable races.