I don't think it is possible to make Cthulhu Woke and stay true to the fiction Lovecraft produced.
Lovecraft was a bigot. It informed a lot of his writing. For good or ill. But he did give birth to a particular kind of horror.
Cosmic horror can be done better these days. New authors can use the basic themes Lovecraft originated to create something new. And honestly? They should.
I just don't think rewriting Call Of Cthulhu is the correct approach. I believe it should be left as it is. Flaws and all. So future generations can learn from it.
The Call of Cthulhu RPG has never been very true to the fiction that Lovecraft produced. It's always been a horror RPG that draws some of the trappings of Lovecraft and some of the themes, but also from Lumley and other writers and its own approach. Further, over the decades there have been a lot of different variants that mix Lovecraft's writing with other sources and genres -- like Delta Green (mixing in flying saucer mythology), Victorian horror, Pulp Cthulhu, and many others.
For example, with regard to the Deep Ones... In Pulp Cthulhu, it's about square-jawed American heroes punching out Nazis and the horrors like Deep One they work with - clear good vs evil fight. That's obviously and intentionally opposed to Lovecraft's cosmic horror, in my opinion.
Lovecraft's stories aren't about good humans fighting against the evil monsters. He much more often had that the horror was that the evil was all around us all the time, and that humans themselves were evil and/or monsters themselves.
In the last CoC campaign that I GMed, I took an approach opposite to Pulp Cthulhu. The game was set in an alternate 1940s just after the Deep War, a devastating worldwide war with the Deep Ones. Part of the idea here was that players didn't have to play dumb, because the PCs knew about Lovecraftian horrors. In the Deep War, the Allies were the great naval powers: the U.S., Britain, Germany, and Japan. The Soviets and the Chinese were neutral. This had a much more uncomfortable feel, as the U.S. had a reluctant alliance with Nazi Germany. The Nazis had a particular hatred of Deep Ones as they produced mixed-race abominations. I think this was closer to Lovecraft's writing than Pulp Cthulhu, though it also had its own take.