Is there a word for a fictional character who's obviously a copyright friendly version of another character?

I believe this would be considered a ripoff or a knockoff character.

You can see some examples here.

A name for your character might be a clone, or a close clone. A clone is described in MW, 2nd meaning, as a copy or duplicate. TvTropes does call such a character a Captain Ersatz, as Emily Murphy points out.

"Clone" may be closer to the word you seek than ripoff, which is an intentional deception. The term knockoff is extensively used in the fashion industry; some knockoffs may be marketed as genuine and other may not.

Whether a comic book character that's copied from an existing character, or is heavily based on an existing character, violates a copyright isn't known when when the comic including the character is published (although a lawyer may be able to advise). Here's a paragraph from Wikipedia on a major case:

National Comics Publications v. Fawcett Publications, 191 F.2d 594 (2d Cir. 1951). was a decision by the United States Court of Appeals for the Second Circuit in a twelve-year legal battle between National Comics (also known as Detective Comics and DC Comics) and the Fawcett Comics division of Fawcett Publications, concerning Fawcett's Captain Marvel character being an infringement on the copyright of National's Superman comic book character. The litigation is notable as one of the longest-running legal battles in comic book publication history.

I believe the character described by your example is actually a Captain Ersatz (per TV Tropes).

Japanese Man 1: Run! It's Godzilla!
Japanese Man 2: It looks like Godzilla, but due to international copyright laws, it's not.
Japanese Man 1: Still, we should run like it is Godzilla!
Japanese Man 2: ...though it isn't. [winks at camera]
— Austin Powers in Goldmember

"Ripoff" or "knockoff," as suggested earlier, are perhaps the most applicable terms in this case. I don't think an "official dictionary" term currently exists that singularly and specifically refers to a thinly veiled ripped-off fictional character.

It might be called a homage:

The term is often used in the arts for where one author or artist shows respect to another by allusion or imitation; this is often treated and pronounced as the French hommage.

Or if it's comic, exaggerated, tongue-in-cheek, then it's a parody:

A parody (also called a spoof, send-up, take-off, or lampoon) is a work created to imitate, make fun of, or comment on an original work—its subject, author, style, or some other target—by means of satiric or ironic imitation.