DBIx::Connector creates your database handle, which you can then pass directly to DBIx::Simple. So, for your purposes, something like this should work:
#!/usr/bin/env perl
use strict;
use warnings;
use DBIx::Connector;
use DBIx::Simple;
my $nms_host = 'mysql.server.com';
my $nms_base = 'mydb';
my $nms_user = 'myuser';
my $nms_pass = 'password123';
my $nms_dsn = "DBI:mysql:$nms_base:$nms_host";
my $conn = DBIx::Connector->new(
$nms_dsn,
$nms_user,
$nms_pass,
{ RaiseError => 1,
mysql_enable_utf8 => 1,
}
);
my $simple = DBIx::Simple->connect( $conn->dbh );