I buy organic ham & as Suse said if you choose a butcher who does his own you can make sure it has no nitrates.

Tuna (though I have an issue with the cruelty aspect) is yummy & low in mercury.

Have you thought of perhaps just slicing tomato and cheese, grating carrot, cucumber and putting them in a separate container to make their own with fresh bread?

My kids go to a vegetarian school so I do wraps with lettuce, cheese, carrot and mayo. They really love them.
I make muffins with spelt flour & no eggs - just some ideas.