I've done some more research on this question, and here's what I've come up with...
Note that he is listed in the IMDB credits for Trial of the Incredible Hulk, even though he wasn't credited within the film itself.
The earliest cameo listed on this page was in Trial of the Incredible Hulk (1989), a TV movie. His earliest listed cameo in a film which received a theatrical release was in The Ambulance (1990).
3) Stan was not mentioned in Richard Donner and Tom Mankiewicz's commentary for the scene, on the DVD of Superman II: The Richard Donner Cut.
Here's a transcript of the commentary for that scene:
MANKIEWICZ: Now here again this is almost like you would do this in a Clint Eastwood movie. And I told Clint once, I never forgave him in Bronco Billy for not coming back and punching out that sheriff who threw him out of town early on in the movie.
DONNER: Yeah, but that's a different movie.
MANKIEWICZ: Yeah, but you gotta be very careful, because this is Superman now, and he can't beat this guy up. So you play it for comedy and--
DONNER: Well, you play it straight.
MANKIEWICZ: Straight here, but Chris' one line: "I've been working out."
DONNER [Reacting to the trucker being spun around on his stool]: Tilt.
MANKIEWICZ [Reacting to Clark handing a wad of cash to the diner owner]: Again, you gotta be very careful that he pays for the damage, everything; this is Superman now.
4) Several websites state that Stan Lee's first ever DC cameo was in the animated feature, Teen Titans Go! To the Movies.
5) There are visible differences in physical appearance between that actor and Stan.
Here's a close-up of the actor in question, from the diner scene.
And here's a video of the diner scene.
Now here's a photo of Stan as he appeared around 1977, the same year the diner scene would've been shot (much of the footage for Superman II, including the diner scene, was shot by Richard Donner during the production of the first Superman film). This photo couldn't have been taken any earlier than 1977, as the Superhero Women book on his desk was published that very year.
And here's a video of Stan making an appearance on CBC-TV's 90 Minutes Live in 1977.
As you can see, the actor in the diner scene appeared to have blonde hair, parted on the right side of his head, whereas Stan had dark, greying hair at the time, parted on the left side of his head. There are also differences in facial structure, particularly the nose and jawline, and the actor looks a bit younger than Stan, with a slightly heavier build. Stan was 56 years old at the time, and relatively slender in build.
6) I've been unable to find any clear indication that Stan appeared in Superman II.
I realise an absence of evidence that he was in the film doesn't prove he wasn't, but if he was in the film for the sake of argument, doesn't it seem strange that there'd be no clear reference to that fact anywhere on the Internet? Even if we suppose that he deliberately altered his appearance for this alleged cameo, so he could could sneak it past Marvel Comics, wouldn't it surely have been noticed and picked up on by various fans and industry commentators in the 40-plus years which have passed since? It's not like we're talking about some obscure, overlooked film here. It's also not like he was heavily disguised in the scene (if that was him, which I don't believe it was).