After a *very* cursory glance, Mime::Lite shows that there are fields other than To.

Bcc (ie. Blind carbon copy) is what you want.

When in doubt, read the documentation (RTFM!!).

So, set To to yourself or blank, and dump all others into the Bcc field.

Besides that, don't use ALL CAPS for variable names, unless they are constants. It's a poor practice to use all upper-case variable names like you have. This is consistent in Perl, and nearly all other programming languages.

Update: ...and where's your use strict; and use warnings;? Is this just a code snip where your variables have already been declared, or do you simply not pay attention to what's been presented to you time-and-time again?