Vacuum and a brush will do the job

You can clean a box fan grill without removing the motor using a vacuum and a soft brush.

The main trick is to not get the motor wet. Box fans are cheap, but the motor is sealed loosely—dump water in there and you’ll either short it or rust the bearings.

Start by unplugging the fan. Use a vacuum with a brush attachment on the front and back of the grill. That handles loose dust and cat hair. For stubborn grime, use a stiff paintbrush or an old toothbrush to agitate the dust while you vacuum. Works for the blades too, if you can reach through the grill.

If you need a deeper clean, use a barely-damp microfiber cloth with a little dish soap. Wipe the grill ribs front and back, never letting moisture drip into the center hub where the motor lives. Let it dry fully before plugging back in.

Just don’t spray anything directly into the motor.