My shop has been heated and cooled with a window style heat pump mounted high and through the North wall of my shop for the last 15 years. Early on I realized that the finer sawdust in the air was building up in the coil fins, so I cleaned it with coil cleaner, water, and compressed air. Then I began looking for a better filter than the cheap foam one that came with it. After some looking and trying, I came up with a 12 X 20 X 1" pleated furnace filter, and it fit between the plastic front face and the coil of the heat pump. I've been using these ever since, with no further need to clean the coils. I buy the better quality paper type filters with heavy pleating and each lasts me about a year, if I take it outside and blow it out a few times over the course of the year. Since there is no real good way to attach the filter, I just turn the unit on with the cover removed, and then place the filter over the coil. The fan suction holds it in place until I get the cover installed. The cover to filter gap under the cover is very close, so the filter never moves after the cover is in place.
Jay Bates, a woodworker of Youtube fame put a ductless unit in his new shop, and then made a large box on the wall that is attached to the intake of the ductless unit. The box holds several 20 X 20 pleated furnace filters. One might consider doing the same or similar for any window style or ductless system to prevent fine sawdust build-up in their system. My unit doubles as my shop air filtration system too.
Charley