The cone and suspension are usually very strongly glued to the speaker chassis, so there is little hope of removing it without destroying it.
You might be able to get the dust cap off and back on again, that will gain you visual access to the coil to see how burnt it is, or not.
But there isn't really a good chance of repairing it, a recone involves ripping everything off, cleaning all the glue off the surfaces, and installing a new cone, coil, suspension and dust cap.
I have in the past done, and seen done, a temporary repair where the braids have been damaged by over excursion, they will sometimes fail open circuit either at the speaker terminals or at the point they go through the cone to the coil.
But it's an unreliable bodge at best, given the abuse the repair has to cope with.
A 9v battery is useful for testing speakers, connect it and wiggle the braids about to see if you can get it to go Pop Bang Crackle.