You don't have to skim the milk for mozzarella. I do because I don't ever get enough cream for other purposes.
I've been making
Lancashire lately and the recipe I've been using has three and a half gallons of whole milk and 1/2 gallon of skimmed. I bump it up to a five gallon batch and I don't skim the milk. It is good at 4 weeks, but much more flavorful at 8 weeks. My first one is about 10 weeks old right now, so has another two weeks to go before we try it again.
Hm, too much cream...wish I had that issue!