Fine-grit sandpaper (often 220-grit or higher) is used to smooth the curved bead and clean the sharp groove of the quirk after machining.
A simple, shop-made tool used to "scratch" the bead and quirk profile into wood, particularly useful for custom or curved work. Customer Questions & Answers - Amazon.com bead and quirk
Heavier cardstock or stiff paper is used to create templates for duplicating profiles across multiple trim pieces. Specialized Tools for Bead and Quirk Fine-grit sandpaper (often 220-grit or higher) is used
In woodworking and architecture, (not wax paper) is commonly used to protect surfaces and tools when creating decorative profiles like a "bead and quirk". Specialized Tools for Bead and Quirk In woodworking
Modern workshops use quirked beading bits to achieve the same rounded edge and recessed shadow line on table aprons or cabinet doors.
If you are working with this specific profile, the "paper" involved typically serves one of these purposes: