Been there, done that. ^_^
I did it because I was integrating the Cthulhu pantheon into my world as a herald for the apocalypse. Tentically fun!
The sorcerer of the party gained some cultish status, and was given a CoC spell. I gave it to him as sort of a "bonus spell." It didn't count against spells known, and he could use it even when out of magic, but he had to pay the cost...
I think this would work well. The back of the CoCd20 book gives rules for spell levels that the CoC spells would be at. I'd use that as a guideline...I wouldn't limit them to class or race or anything. Anyone who was touched or did the research could cast the spells. As a DM, I'd probably limit them by character level...roughly, a character of twice the level of the spell in question could gain the spell. So, a 4th level CoC spell could be learned by an 8th level character, be it a fighter, a sorcerer, or a cleric. And whoever learned it could use it basically "for free," simply by paying the ability score cost.