Kanga, if you want to keep the family and really do trust them then I agree you shouldn't offer any milk products at all to the child until the doctor's diagnosis. If it were me I wouldn't give him any cheese, yogurt or other milk products either just to be safe.
I had a little girl with a nut allergy in my daycare for a few years and it isn't that difficult to read labels and make sure you keep an allergic child safe. It just takes diligence in everything you do and everywhere you go which is part of our job because we are awesome. It can be done.