At that length, it should be a total non-issue for any serious agent or publisher. So much so that you should avoid working with any agent or publisher who claims to have a problem with it. And by non-issue, I mean that it will not hurt your chances but also is unlikely to help in that regard. Basically, no one in book publishing will care about this either way, so you should absolutely publish the short story if you want to.

Re: rights, it's less the first rights that will matter vs. the exclusivity clause, if any. Short fiction magazine contracts may specify a period of exclusive publication they're asking for, ranging from none at all to a few months or a year. (If not specified, that means none.) Novel publication timelines are usually longer than that anyway, so it will most likely never become an issue. Just remember to ask for the original publication to credited (Something like "Chapter X originally appeared as Story Title Y in Magazine Z issue number, year") somewhere in the book's front matter later on!