Add my votes to those who’ve said Tom Verlaine, Bob Mould and D. Boon. I’d like to nominate Robert Quine, though I don’t know if he’d count.
I love his guitar playing, but in no way his style resembles new wave/punk. Same applies to Mike Campbell. They just became popular at the same time as punk.
I was thinking the same thing…his work with Richard Hell & the Voidoids was amazing, though.
The Honeyman was amazing - an awful loss way too early. Nice catch. I was going to mention Gill in my first post, but held off for some reason…well, because he purposely chooses a harsh, grating tone - hard to take at times, but that was a choice he was making. The intro to Love Like Anthras - a fave or mine - sounds like he is drilling metal on metal…
Stuart Adamson deserves a honourable mention, I think.
Although I gave my vote to Tom Verlaine in the OP, I think that Thurston Moore and Lee Ranaldo (you can’t separate them) deserve a mention. Both certainly influenced by Verlaine (and Richard Lloyd), but as inventive and stylistically unique as him.
More noms:
Bob “Derwood” Andrews from Generation X
Um, Paul Weller?
Great songwriter, but exceptional guitarist? I don’t think so.
Disagree - in a Kurt Cobain-y, Pete Townshend-y, Alex Lifeson-y, Billie Joe Armstrong-y approach, he filled out a three-piece lineup very effectively. Not as flashy as gunslinging, but, speaking from experience, very hard to do.
Different from EVH, Hendrix, Page, Clapton/Cream supergroup three-piece guitar playing…
The former kind of “sonic layer that’s a foundation to the song” rhythm guitar player is real inside-baseball muso stuff that a lot of non-players don’t appreciate. No offense at all, just trying to provide a player’s perspective…
So yeah: go Paul Weller.
OK, after thinking about the points you made (and thinking about his music), you convinced me. And I love “Days Of Speed”, where he proves that he can take the stage alone with only an acoustic guitar and make a hell of a sound.
I’ll second the nomination for Johnny Ramone. Watching that guy play was an awesome experience.
Honeyman-Scott, Verlaine, Quine…you can’t really go wrong with any of them. If you want someone with a bigger catalog, maybe Ron Ashton.
I’ll third or fourth Billy Zoom, and thrown in Fred “Sonic” Smith.
Man, I was going to say Dr. Know and Robert Quine but I was beaten to both of them. Allow me to repeat those nominations then.
Gotta put Pat Smear and Paul Leary in there somewhere.
Oh, if Brian Setzer counts, he’d be a very strong contender, but you’d have to be pretty generous to count him in.
Good analogy, maybe there needs to be a “best musical utility infielder” thread. 
I love Brian Setzer and think he’s a great rockabilly/jump blues guitarist but I’m not sure The Stray Cats really fit in New Wave genre.
I’m going to make an offbeat nomination: David Byrne. People really don’t think of him as a guitarist but rather as a singer and oddball frontman. However, I just re-watched “Stop Making Sense” a couple of weeks ago (best rock concert movie EVER) and I was really struck by what an excellent rhythm guitar player he really is. He can really lock on a groove with driving force.
Also, seconding Andy Summers, Bob Mould, Mick Jones and Joey Shithead (the only one I was lucky enough to see play live).
You have a good point, as I also usually think of David Byrne as more of a frontman/vocalist than for his guitar playing, but I saw him in concert twice this year, and was also very impressed with his work on the guitar ( I think he plays a Fender Stratocaster?)
Someone upthread mentioned David Hidalgo (Los Lobos) and while I dont usually first think of Los Lobos as a new-wave band, I guess that they do have a proto-punk meets Americana meets Guadalajara garageband thing going for them.
In any case, David Hidalgo is a great musician, no matter what genere one would place him in.
(A couple of years ago, I saw Elvis Costello and David Hidalgo play together down in New Orleans, and it stands as one of the highlights in my 25+ years of travelling for live music)
Howsa about we limit the discussion to guitarists who either cut their teeth in the new wave/punk/american hardcore scene or were best defined by that.
For example, Robert Fripp should not be part of this discussion, while Bob Mould and Andy Summers should.