Sympathy solo and also the lead guitars on Stray Cat Blues is just a really piercing trebley, slightly fuzzy/distorted sound most likely achieved via the Brilliant channel on a Vox Supreme.
They used Vox Supreme's and related amps(not exclusively) from 1967 European tour, Their Satanic Majesties Request, Beggars Banquet and possibly some of Let It Bleed as one can be seen at Redlands in spring 1969.
Screen grab from One Plus One, Vox Supreme on the right.