Just curious, what's unclear in the docs of LWP::UserAgent?

$ua->proxy($scheme, $proxy_url)

    Set/retrieve proxy URL for a scheme:

  $ua->proxy(['http', 'ftp'], 'http://proxy.sn.no:8001/');
  $ua->proxy('gopher', 'http://proxy.sn.no:8001/');

    The first form specifies that the URL is to be used 
    for proxying of access methods listed in the list in
    the first method argument, i.e. 'http' and 'ftp'.

    The second form shows a shorthand form for specifying
    proxy URL for a single access scheme.
[download]

In your case, it seems that you can use the second, simplified form just like merlyn pointed out.