You can just use 'exit' instead of of a CTRL-Z.

sub update_router_config {
  if( $cisco->enable("$enable_password")){
        $cisco->cmd("config t"); # enter new configuration
        $cisco->put("$conf");    # send new data for config
        $cisco->cmd("exit");              # end new data
        $cisco->cmd("copy run start");  # enable new config
        }
}
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-Vlad