Two suggestions based on discussion from CB:

while ($string =~ qr(...)) {
    $string = qq($1'$2);
}
[download]

and

$string = join('_',
    map {
          ( $_ && ( $_ !~ qr(') ) )
        ? qq('$_)
        : $_
    } split( q{_}, $string )
);
[download]

The first, I think, is O(N^2), and the second is O(N), so depending on string size, data set size, etc, the choice might make a difference.