I'm assuming that you want no verification done, so using SSL_verify_mode => 0x00 can be as simple as using the SSL_CTX_set_verify method. I used the example in the ex dir.

#!/usr/bin/perl

use strict;
use warnings;
use LWP::Simple;
use IO::Socket::SSL 'debug0';

$|=1;

IO::Socket::SSL::set_ctx_defaults( 
     SSL_verifycn_scheme => 'www', 
     SSL_verify_mode => 0,
);
print get( 'https://pause.perl.org' );
[download]

First, you want to make sure that you don't use debugging because that'll call in ciphers from Net::SSLeay and call Net::SSL, which you don't want to use. Then set IO::Socket::SSL::set_ctx_defaults.