After I posted, I had a nice conversation with a couple of the workers in the meat and deli departments of my local supermarket. The fellow in the meat department said that they could not slice a pepperoni stick because of cross contamination issues. However, they can run, say, a smoked or cured ham or turkey through their slicing equipment but only at the end of the day after they clean and sanitize their equipment that they use to cut beef, pork and other uncooked meats. That means they need about 8 hours lead time. When they are done, they then have to clean and sanitize their equipment again. This service is only offered to their customers who purchase the items in question at their store. There are apparently people who bring in hams and the like purchased from Wal-Mart or Costco's and ask the workers at my supermarket slice the items for them. There is no upside for the supermarket to do this. There is only a downside (like a lawsuit if something goes wrong).
The worker in the deli department said that they would slice pepperoni sticks but, again, only if purchased at the store. They have no cross contamination issues because all of their deli meat products are cooked.