I do. The Spock, Chapel, Uhura, Gorn, T'Pring and Kirk (and to a lesser extent Pike) of SNW are not the same as those of TOS, by design. Not merely the actors (no kidding) but the characterizations and backstories as well. That is neither surprising nor objectionable; a 2025 production need not be beholden to a 1966 one. But for some of us it means the loss of at least a portion of the things that got us to love Star Trek in the first place. For me, TOS is a distinct idiom that can't be recaptured simply by naming characters Kirk, Spock, McCoy etc.
If what you are saying is that you think you can write a book that is ambiguous enough to be both a TOS tie-in and a SNWified Kirk & Co. tie-in (as per the preferences of the individual reader) I have my doubts, but hey you're the writer--I'll give it a chance before I pass judgment.