Check out Australian singer David Campbell's YESTERDAY IS NOW album, available at iTunes. He covers R&H, Craig Carnelia, Amanda McBloom (pop, but her songs could be show tunes) and Irving Berlin. And then there's a medley from Australian musicals, but that may be a little rowdy for your party.
I can heartily recommend any of Campbell's albums, but that particular one has a lot of show tunes.
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While I'm at it, let me recommend you check out Steven Pasquale's "Maybe" from ANNIE, on his solo album. He sings it as if it is about a lost love, rather than missing parents--which strains credulity a bit with some of the lyrics (his lost girlfriend collects "ashtrays"?)--but party guests aren't going to be following that closely. But it's a beautiful rendition of what IMHO is the best song from ANNIE.
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Finally I assume you know that the great mid-century pop and jazz singers were all singing show tunes, yes? So almost anything from Billie Holiday, Frank Sinatra, Nancy Wilson, Keely Smith, Nina Simone ("Feeling Good" for just one example), and Diahann Carroll--I could go on, these are just a few of my personal favorites--will fit your criteria.
And in this century, almost every Broadway performer of any note has recorded at least one CD of old show tunes, so check for your favorites on iTunes.
Have fun! I put together something similar for our wedding--and that was before the easy access of iTunes--and had a blast! You can influence the "through-line" of a party greatly with a good soundtrack.