I'm not sure that 4" would be a large enough size to do any good. I would suggest having the HVAC contractor look at it. At least find one who would tell you how to do it for $100 or less for a service call if you want to DIY. That would be part of the heat exchanger installation and maybe that contractor can help you on the fresh air intakes as a part of or instead of the HE. I think heat pumps are overrated except maybe in the northern tier of states.
I think it would help but condensation has many causes and not all are easily fixable. I don't think anyone can tell you it will get rid of all of it. Some will still help. Good luck.