In canada I’ve seen people biking, and even working out at a gym using half mask respirators with cartridges. I have one for doing certain kinds of work, but they are easily breathable and very lightweight. Just get a cartridge/filter for pm2.5 p100. Your face will sweat, but your lungs will thank you. They’ll be more and more necessary in the future anyway.
I’ve seen this idea in leeward areas of California wildfire smoke, and while it should work, the caution I would give is to either find a mask which has little air resistance when breathing through it, or to be mindful of that restriction and not try to go all-in on exercise. Masks are breathable and effective at intercepting particulate matter, but I don’t think they’re tested for the sort of heavy, rapid breathing from exercising. And the longevity of the filters under such heavy loads is unclear.
But it’s certainly worth a shot. Just make sure the mask is still snug, since a loose mask will diminish effectiveness.
A proper fitting is essential. You should test every time by blocking the intake to see if there are leaks. Facial hair will prevent a proper seal.
I use 3M 2097 filters. They’re good for particulate and organic vapours. Very breathable in highly physical environments in my experience. Extremely lightweight.