Based on the documentation for scan() I have put together this basic PoC which works for me:

#!/usr/bin/env perl 
use strict;
use warnings;
use HTTP::Cookies;

my $jar = HTTP::Cookies->new(file => 'cookies.tmp.txt');
my $nsjar = HTTP::Cookies::Netscape->new(file => 'netscape');
my $copy = sub {$nsjar->set_cookie(@_)};
$jar->scan ($copy);
$nsjar->save;
[download]

This assumes your existing LWP jar file is 'cookies.tmp.txt' so obviously change that to the real path you use. It creates a new jar in Netscape format called simply 'netscape'. I did not attempt to do the same for MS cookies but would be very surprised if the same technique did not apply there.