Well, you probably want to test for defined eval { fileno $fh }...

$fh = \*STDIN;
print "Nope\n" unless eval {fileno $fh};
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It still doesn't really work, though. This must be the first example of code that doesn't work with no strict! Try this:

$fh = 'STDOUT';
print "Nope\n" unless defined eval {fileno $fh};
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This prints <samp>Nope</samp> with strict (can't use string as symbol ref), but not without strict...