1. Is it a Sunnah to say ‘Alhamdulillah, yaghfirullahu lana walakum’ when shaking hands?
2. Do both people shaking hands say this du’a, or does one say ‘Amin”?
1. I haven’t seen these exact words as a recommended recital for handshakes. However, it seems like this is derived from a Hadith in which Rasulullah (sallallahu’alayhi wasallam) said:
‘When two Muslims meet, shake hands, praise Allah and ask Him for forgiveness they will be forgiven.’
See here for the reference.
2. There is no harm in either of these two options.
Note: It is important to note, that since the Hadith does not specify what words to use, the ones cited in your query are not binding. Although there is no harm in saying them, praising Allah and seeking His forgiveness can be done with other words as well.
And Allah Ta’ala Knows best,
Answered by: Moulana Muhammad Abasoomar