Your Submission, Starring The Manuscript You Wrote in College

A thousand years ago when I was in college I entered and happened to win a literary competition at my (tiny) university. The prize was publication in the university's literary magazine. The circulation of the magazine has got to be under a thousand, and it only came out annually. (Or, at least, this was true then and I assume it still is.) There was no payment, nor was there ever any discussion of what rights they had and what rights I retained. No mention of anything like copyright was made in the fine print of the "magazine" itself. I'm not asking whether I can claim this as a publication credit. I know better than to try that. But for years, I've never done anything with this story again, even though I think it's a pretty good one, because I'm not sure what I can actually offer, and I'm afraid that trying to convey the situation will make me come off as amateurish. Can I safely submit the story without ever mentioning its "publication" history, tacitly selling first North American rights or whatever?

You should be honest about its publication history. But as you gave that college publication no rights, they have no rights. (You may want to write to them to make sure they understand this, though.)

Will mentioning that it's previously "published" make it undesirable because it's a reprint?

It wouldn't to me, but I can't speak for everybody.

Worse, will it make me look like I'm trying to pass off my small time college lit mag as a real credit?

This will simply depend on how you present the information. If you're just letting editors know the history of the piece, that's fine. If you're boasting that it was in a college magazine, that's eye-rolling. It's the difference between a footnote and a headline.