I'm inclined to think that handshaking was not common in the era. At least not for two people who lacked a reason to be intimite.

In Tarlton's case, it might be a case that he might meet scores (or more) people a day who wanted to demonstrate their "regard" for him by offering their hand. (Including those who would like to be able to boast of having shaken the hand of a national hero.) An injured hand provided an excuse (without any insult) for overzealous fans.

I remain,
Jason E.