Quite the contrary, I would not expect a high end contractor -- if that is what OP is using -- to accept CC's and would associate that more with the guy installing a new sink.

It isn't as though this guy is refusing OP's request, it's that he doesn't take CC's at all. Thus, in order to process the charge, whether OP pays the interchange fees or not, he has to go through the entire sign up process for a vendor, purchase a chipped reader and the like (because it's not likely that a contractor will be eligible for Squared or one of the small sub-vendors).

As to chargebacks, this comes down to region and demand. If the guy is in demand, the first thing he would be told is not to take CC's because it is a hassle and brings out exactly the customers one wants to avoid. That isn't to say that OP is a "bad" customer who is going to nickel and dime a chargeback because there is some minor blemish,

I would focus on quality and price before the CC issue.