What is a substitute for milk when making ham balls?
As ChrisH said in the comments, probably all that matters is that the milk is a liquid. If the end result is supposed to be something solid, there can't possibly be that much milk in there, and the fat and flavor of the milk are pretty small compared to the meat.

So, just use another liquid. If you're not worried about flavor, water would work. Stock/broth might be a nice small step up. Or if you want to tweak the recipe, you could take the opportunity to add other flavors. There are plenty of flavorful but mostly water things you could try - think of things like worcestershire sauce or soy sauce (though I'm not sure what'd go with your recipe).

If the recipe calls for the milk to be mixed with bread or something else starchy (like this recipe, for example), that's called a panade, and it indeed works with all kinds of liquids.