This may do. Lightly tested. XML::LibXML seems to normalize attribute names to lowercase. (update: cleaned up loop a little.)

use warnings;
use strict;
use XML::LibXML;

my $parser = XML::LibXML->new;
$parser->recover_silently(1);
my $doc = $parser->parse_html_file(+shift||die "give an HTML file\n");

for my $link ( $doc->findnodes('//link[@rel]') )
{
    next unless lc($link->getAttribute("rel")) eq "stylesheet";
    print $link->getAttribute("href"), $/;
}
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