Try something like:

package Foo;

...

sub sort {
    my $self = shift;
    my $code = shift;
    sort { $code->($a, $b) } @{$self->{arrayref}};
}

my $foo = Foo->new;
$foo->sort(sub { lc($_[0]) cmp lc($_[1]) });
[download]

I know it's not as pretty, but it should work.

How does Perl's built-in sort manage to be prettier than code you've written yourself? The answer's in the question!