Unless they do something different in the Italian vs salami versions of their grinders, the dressing is just plain salad oil. Once years ago I asked if they used any special oil, and they told me the brand name–one all would recognize. Mixed in your case with mayo it would form its own kind of dressing along with the s&p, if you answered yes to that.
This is making me hungry!! I am looking forward to the last weekend of the month, when my sister and some other family members will be visiting. I’m hoping they stop at D’elia’s on the way up from NJ.