This is not a perl issue, but a quick search reveals some CSS might help, as in the following:

my $q = CGI->new();
print
    $q->header(),
    $q->start_html('Fixing the width of a <select> widget'),
    $q->h1('Fixing the width of a &lt;select> widget'),
    $q->start_form,
    $q->scrolling_list(
                       -name     =>'constraints1',
                       -width    => 300,
                       -style    => 'width:300px',
                       -size     => 12,
                       -multiple => 300,
                       -values   => [],
                       ),
    $q->p(),
    $q->scrolling_list(
                       -name     =>'constraints2',
                       -width    => 300,
                       -style    => 'width:300px',
                       -size     => 12,
                       -multiple => 300,
                       -values   => [1..20],
                       ),
    $q->end_form(),
    $q->hr(),
    ;
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