Though I haven't purchased Zephyr skin in several months you might
check out the following as possible sources of supply:

Player Piano Co., Inc.
704 E Douglas Ave.
Wichita, KS 67202
Phone: 316-263-3241 or 316-264-0033
Fax:   316-263-5480
http://www.playerpianocompany.com/ 
  Item #60, Approx. 24" x 8" sheet
  Last known cost $49.00 per sheet

 [ Player Piano Company ceased business when Durrell Armstrong died
 [ in December, 2008.  Some of the inventory was sold at auction,
 [ the remaining merchandise is now sold by
 [   Player Piano Parts, Inc.
 [   701 E 2nd Street North
 [   Wichita, KS 67202-2713
 [   tel.: 1-316-263-3241
 [   http://www.player-piano-parts.com/ 

The Leather Supply House
345 Hazel Avenue
Garwood, NJ  07027
http://www.leathersupplyhouse.com/ 
E-mail: mike@leathersupplyhouse.com.geentroep [delete ".geentroep"]
Phone: 908-389-1000
Fax:   908-789-0647
  Zephyr membrane (X-Thin .001-.002), Approx. 9" x 15" sheet,
  Other thicknesses also available.
  Last known cost $21.50 per square foot

Most sincerely,

Don Caine - Proprietor, The Music Box Repair Shop Unlimited
Lomita, California
http://www.musicboxrepaircenter.com/ 

P.S. I specialize in Reuge and Thorens Vintage music box repair and
restoration.  Please let me know if I may ever be of any service to
you in identification, repair or parts for music boxes you may have,
or come across in your business.