Shaking on Saturday

Good week Rabbi,
Let's say there are two friends, one is strict about shaking hands on Shabbat according to the Maimonides' method (which the public domain of the Torah does not require 60 rabbis to be removed from it – and therefore the municipal eruv does not apply to regular streets), and the other is lenient about shaking hands on Shabbat according to the Rashi method (which the public domain of the Torah is only if 60 rabbis are removed from it). Can the strict friend ask his lenient friend to shake a siddur for him to the synagogue? Or is there a blind person in this according to his method?
Best regards,