Take one of the screens and just add plexi/acrylic/plywood to the side that won’t interfere with fitting back on the window and I wouldn’t even bother removing screen if it’s not needed.
Those screens are meant for bugs so I would add some sort of material to seal against blowback on the frame against the window like thin foam or felt that would make it easily removable. Once you have that working I would then add the exhaust components.
But even with all that and a booster fan you will still have some lingering smells or fumes that although not that harmful could easily offense people with a sensitive olfactory.