Assuming the func() is something complex, possibly involving $thing several times, you'll have to name $thing somehow, no matter what the syntax. Most likely $_, right? So why don't you do just that?

print foo($_) ? $_ : 'undef' for fileno $fh;
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You can't get it much shorter without getting it way too confusing. I understand you want to get rid of the ": $_" bit, but I don't think you can nor should do that.