In woodworking and architecture, (not wax paper) is commonly used to protect surfaces and tools when creating decorative profiles like a "bead and quirk".
If you are working with this specific profile, the "paper" involved typically serves one of these purposes:
Modern workshops use quirked beading bits to achieve the same rounded edge and recessed shadow line on table aprons or cabinet doors. bead and quirk
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
Heavier cardstock or stiff paper is used to create templates for duplicating profiles across multiple trim pieces. Specialized Tools for Bead and Quirk In woodworking and architecture, (not wax paper) is
For craft beads that might use similar terminology, parchment paper is the standard barrier to prevent sticking.
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. Customer Questions & Answers - Amazon
Antique or specialized wooden hand planes are the traditional method for cutting these profiles in a single pass.