Hi there,
over time, many German names were anglicized in spelling, and perhaps the family was once Scheier? Your search name, Shire, would then be a phonetic spelling of it. There are loads of entries under Scheier on the internet, such as houseofnames.com, ancestry, hebrewnames.com, etc. Maybe this helps. If it's Jewish in origin, it could have derived from Scheuer (scheuern (verb) = to scrub, clean hard.)
Happy hunting!
Kathrin :o)