a draper was a better quality shop ... would custom make dresses

This came to me overnight :
In dressmaking sometimes the designer would drape the customer with the fabric to see how fabric "draped" and whether or not the color suited the customer.
Additionally sometimes tailors would (will) drape a model with muslins from which a pattern was cut.
The word "muslin" - in the world of couture - has two meanings 1. the fabric itself; and 2. the designed garment made up in a muslin fabric, sewn with stiches easily pulled out, leaving the pieces perfectly fitted to the person which is then used as a pattern for making up the garment in the more expensive fabric.
Muslin is a finely woven cotton fabric, usually a sort of ecru color, which (I believe) is sometimes used as an inter-lining in hand crafted men's suits.
Whew! See what you learn when you have a friend who worked on Seventh Avenue?

For non-US'ns 7th Avenue, New York City, is the heart of the Garment District.

AEnigma wants "men's" to be menace. Hmmmmm. Perhaps it is just men in drapers' shops?