You could use a ERV. Pull air from the shop and return it to the apartment.
Interesting thought. If you'll be air conditioning, an ERV makes sense. If not, an HRV makes more sense. Keep in mind that both neither deals well with dust in the air, so exhausting shop air may become an issue unless you add a filter.
For those not aware, these have two air inlets and two outlets, with an inlet and outlet outside and another pair inside. The idea is normally to exhaust bad air from inside, while simultaneously taking in fresh air from outside in a balanced way so that air doesn't get pulled through other openings in your structure (unlike a plain exhaust fan). The HRV uses a heat exchanger to minimize heat exchange with the outside, while the ERV also handles humidity, so they can be run continuously with minimal heating/cooling costs too.
In your use case, the ERV/HRV would be exhausting shop air, and pulling in the replacement air into the apartment. This would have the apartment at a higher pressure than the shop, driving a flow of air from the apartment into the shop.
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