Quite convincing, when you put it that way... but where did you get these ideas? The gist of HPL canon is that the Cthulhu cult resides mainly in scattered, primitive groups (in West Africa, Polynesia, Greenland, the West Indies, etc.) and has little or no foothold in Western civilization. The fellows at Pagan Publishing extrapolated from this idea, making the assumption that the Cult would not fare well during the transition to the age of jet travel and the internet. Further, the stars were almost-right in early 1925 but haven't been right since then.
I think it's a mistake to view the Cult of Cthulhu through that lens as the "degenerate cult living in the swamp" is just the group which Inspector Legrasse encounters. The cult is an onion which the first layers point at a religion which only "primitives" worship but as we go through the story we gradually come to the realization Cthulhu's worshipers are everywhere and of every layer of society.
In New York City, "hysterical Levantines" mob police; in California, a Theosophist colony dons white robes to await a "glorious fulfillment." Ultimately, the novel ends with Thurston not threatened by a bunch of wild-eyed degenerate backwoodsman but believing he's going to be tracked down and killed by what is obviously a global network.
Then again, I've always taken the Cult of Cthulhu to be a take-that at organized religion and Christianity in particular with The Dunwich Horror a similar religious parody. After all, the Cult of Cthulhu is a religion which worships a dead god of resurrection who will eventually arise to provide the faithful immortality and punish the unbelievers. The religion looks foreward to the end of humanity but is composed of all ethnicities, classes, and countries.
More to the point, they/we needed in Delta Green a central premise that would tie together such diverse elements of modern conspiracy as UFOs, MKULTRA, Moon artifacts, USS Eldridge, HAARP, men in black, and so forth. Hence the Mi-go visitation, instead of the cult of Cthulhu. Oh, and don't forget decrepit Nazi sorcerers.
Ultimately, it's a matter of taste but I find Cthulhu and his cultists to be the singularly coolest part of the Cthulhu Mythos. The ultimate religion of evil existing in plain sight and extraordinarily diverse in its followers. You can have a occult sect of sorcerers, a gigantic church, a rural farming community, Deep One-affected city, billionaires, or weird cultists all paying homage to the same deity and working together.
But of course it's your game and you can do what you want! I'd start by asking whether the Mi-go would be pro or con waking up Great Cthulhu, and how they'd go about using humanity toward that purpose -- or, just write out the fuzzy fungi altogether.
You could also use the Tcho-Tcho as your stock Cthulhu worshipers; connecting them, if you like, with the "undying leaders of the cult in the mountains of China."
I'd love to hear your own ideas
Well, Delta Green indicated they considered it would be a terrible waste for humanity to be destroyed when the Great Old Ones woke up but I don't think they're stupid enough to try to directly oppose Old Bat Wings. As for the Tcho-Tcho I've always felt them to have only been useful in the D20 and updated version where they were a persecuted ethnic minority which had come to live in America with some strange habits.
It reminded me of an episode of Angel where they had a marriage where the groom's ex was to have his brain eaten but otherwise they were a nice bunch of demon-human hybrids.
The first question is whether or not your players imagine a mountain walking or stumbling or a little plushie when you say, "Cthulhu."
My players generally use Godzilla as the starting point for Cthulhu. A big huge kaiju who just happens to have massive psychic powers. Which is a fine monster to punch when you have the Justice League.
When you DON'T...
I also tend to think HP Lovecraft and his works didn't exist in the Cthulhuverse (or Robert Bloch had HPL's doppleganger killed in "The Haunter in the Dark") so there's no plushiethulhus.