Providing your ham, chicken, turkey and beef are recognisable as having come from an animal then they are carb free. These are not bad for you and will not spike you. Carry on eating them.
When people talk of processed food they usually mean super processed food. I offer the kiev as an example. A factory in the Ukraine processes chicken and the unsightly ones get minced up and mixed with stuff to make kievs. When asked how many kievs they could make from one chicken breast they said six. My tests showed that one of them spikes me the same as a Mars bar. The stuff they mix with them is probably rusk.
Other processed foods which should really be avoided are all those things made out of flour and sugar (but no fat) which are packaged very often as ready meals. My local supermarket has shelves and shelves of the stuff.
Having said all that there are some processed foods which are OK like corned beef, Mathesons smoked pork sausage. and even original recipe KFC chicken pieces (with just a few fries).