Your second example looks more correct, but in fact should be:

foreach my $parent (@LWP::UserAgent::Determined::ISA) {
    if ($parent eq 'LWP::UserAgent') {
        $parent = 'LWP::UserAgent::Proxified';
        last;
    }
}
[download]

instead of push.
Module can automate this routine actions and make some additional checks.