I highly recommend, wet Q-tips.
If you need longer the wooden ones go to about 5" in length.
Just use water, as your cone is polymer.
Be sure to stay away with anything metal. I say this with lots of experience. You will destroy your speaker in the blink of an eye.
If you need to get crap out from around the voice coil to magnet, fold a piece of scotch tape, sticky side out, and gently slide it around the gap.
That will usually work, even to get little pieces of metal shavings out.
Please keep in mind to stay away with needle nose pliers and screw drivers.
Also, you can use paper towels on the large parts of the speaker cone, water works fine.
Try cleaning from the center to the outer to keep it away from the voice coil / magnet gap.
That's the most delicate part.
Good luck.