According to the 'ahnaaf it is permissible to shake hands with the 'ajuuz (old woman) and touch her hand if there is no fear of fitnah.
They are alone in this opinion of theirs. The Maaliki, Shaafi'i, and Hanaabilah do not permit you to touch or shake hands with the 'ajuuz regardless of if there is fear of fitnah or not.
Kuwaiti Encyclopedia of Fiqh
Volume 31 Page 55