In principle, it is permissible to shake hands with old women only if there
is no fear of sin and desire from both sides.
Hadhrat Abu Bakr (Radhiallaahu Anhu) used to go to the tribe where he was
breastfed and used to shake hands with the old women of the tribe. (Hidaaya
vol.4 pg.459; Ashrafiyya)
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai