Having difficulty finding pre-packaged cold cuts that don't have some form of milk in them? Are you finding some version of 'lactate' or 'lactid acid' in them? Both of these ingredients indicate milk possibilities and seem to be in most cold cuts, pre-packaged or not. Here's an option that may offer a nice alternative for your family.
Smart Allergy Review of Hormel Cold Cuts
Hormel Natural Choice line, distributed by Hormel Sales, LLC.