I have never heard a modern word for a wigmaker,BUT
in the olden days a wig was often referred to as a Peruke,and the makers of Perukes were called Perukiers.
This link from Manchester Art Gallery might interest you:~
http://www.manchestergalleries.org/our-other-v enues/platt-hall-gallery-of-costume/the-collec tion/collection-themes/narrative.php?themeback =1&CostumeTheme=Dressing+up%2C+Dressing+down&i rn=156
Part of the entry says:~
For over a century from the 1660s to the late eighteenth century, fashionable men chose to shave their natural hair and to wear a wig instead. Over this long period, styles changed, but the procedure remained similar, necessitating the regular services of a barber for shaving, and to powder the wig, and a wig-maker or perukier to provide new wigs, maybe once a year, and to restyle used wigs.