I once asked the butcher at a place where I bought some stick pepperoni whether it was possible for him to slice it for me if I wanted. He said that he would do whatever I wanted, in whatever thickness I wanted. I wasn't planning to use the pepperoni any time soon so I declined. But at least I knew it was possible for him to do it. I think that would be my first choice.
As for using your Cuisinart unit, I wondered also whether it was possible to use one of the slicing blades to slice pepperoni stick. So I went to cuisinart.com and looked at the manuals for a representative sampling of their food processors. The answer in all cases was that hard sausage could be sliced using one of the slicing blades. For salami or other hard sausage (and I assume pepperoni stick would qualify as a hard sausage), the instructions I saw (they were the same for all of the units I looked at) were as follows: "If the sausage is thin enough so that one or two of them will fit in the small tube, use that tube. Or cut the sausage into enough pieces to fit into the large tube completely. Stand the pieces vertically, packing them in tightly so they cannot tilt sideways as they are sliced."
You may want to check the manual for your unit to confirm what I just quoted. I have no idea how thin or thick the slices will be or which slicing blade you should use (I saw 2mm, 4mm and 6 mm blades mentioned for some of the units I looked at). But if you do decide to use your Cuisinart, please let the rest of us know whether it is a viable option.
Another tip I have seen about slicing pepperoni stick manually is to freeze the pepperoni stick for a while before slicing.