What is the cause of the 'bad air'? Is it the finishes, wood dust from sanding or something else? There may be other solutions. If you plan to run your ventilation system for any length of time you are going to be removing all the warm air from your shop.
I would say a combination of both probably. My shop is in my basement, so I'm not worried about my heat.
I have a basement shop measuring 10' x 18' (fairly small) as well with zero air circulation. No windows or exhaust. I run a dust collector and an air filtration system and that takes care of all those 'bad air issues'. There are certain finishes I don't use, such as lacquer, because they linger in the shop and can even bleed up to the main floor of the house. I do use CA in my shop without a problem when I have the DC and air filter running.
If you vent your shop to the outside replacement air needs to come from somewhere. That somewhere will be from the house even if your doors are closed and you will be losing heat. If you open a window in your shop/basement with the exhaust running you will be pulling in a lot of cold air, have a cold shop and probably still be having a small impact on the heat in the house.