Another option is to move the return statement up to the loop, where $black_player has been localized. Then you can explicitly return undef on a failed match like the function comments state. Here's my slightly condensed (and untested) rewrite:

sub find_paring() {
  my $wp = $_[0];
  foreach my $bp (&shuffle keys %{$matches_remaining{$wp}}) {
    if (exists $matches_remaining{$bp}{$wp})  {
      delete $matches_remaining{$wp}{$bp};
      delete $matches_remaining{$bp}{$wp};
      return ($wp, $bp);
    }
  }
  # Else return undef
  undef;
}
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