A man who did this work was called a Shearman or sherman.
"In the Days of the Guild"
Louise Lamprey
On this fatal night, writes Sir Bernard Burke, she dreamt that one Mrs. Shearman-the housekeeper-came to her and asked for a sheet.
"Strange Pages from Family Papers"
T. F. Thiselton Dyer
She demanded, "for what purpose," to which Mrs. Shearman replied, "Poor Master Robert is killed, and it is to wind him in."
"Strange Pages from Family Papers"
T. F. Thiselton Dyer