One would think that masking Thelin's grayish skin would only require a bit of powder from McCoy's well-equipped man-purse...
In any case, a lot of the TOS adventures might have happened slightly differently if there wasn't a high-ranking cold-blooded (or sometimes hot-blooded) touch telepath aboard. But we're not really talking about diverging timelines here. Just as with the Mirror Universe, we are talking about converging timelines. All those universes that result in Thelin being there with Kirk in "Yesteryear" are valid, even if they are otherwise radically different from "our" timeline (say, "their" Kirk is married to the President of Venus, the only surviving habitable planet in the Sol system).
So, how would "City" go if Spock were replaced by Thelin? No touch telepathy needed in that episode, nor cold-blooded logic - Kirk is the one who has to act callous there. It would suffice for Thelin to be able to make the same deductions Spock did about the role of Edith Keeler, who would still be the kingpin to the events. That is, the crazed McCoy would gyrate to Keeler's place no matter who was traveling with Kirk, and would try and save Keeler at the crucial juncture. So essentially, we're talking about the same events, the same episode.
Timo Saloniemi