DON'T SMASH AT IT WITH A HAMMER ! ! ! !

Doing so with any amount of serious impact force will certainly destroy the bearings in the BB and very likely will cause damage to a carbon frame. Take it around to a well equipped bike or car shop and have them use their bearing pullers on it that were mentioned above. Or suck up the loss of time and re-assemble it enough to ride it.

If it were the non-drive side you could set the arm knuckle up against a big block of something heavy to take the hammering forces delivered to the side of the arm. But since this is the drive side and the arm's spider legs are in the way you can't get enough effective force into the arm to split or deform the arm enough to let the crank loosen up. So all you'll do is end up ruining the BB bearings.

As for the frame material if the joints where the tubes join is a big smooth filleted shape then it's likely carbon But if they are an obvious weld joint then no, the frame is aluminium or steel. If in doubt post up some pictures taken of the BB cluster or seat post cluster showing the joints well. If it's metal then bead or other media blasting would be fine. If it's actually carbon then no, you don't want to blast it at all. It'll need to be wet sanded by hand to prep it for new paint. Special care needs to be used to only just barely sand down to the last sign of the original paint or primer and not to go further and sand into the actual carbon layup. In otherwords as soon as you see ANY signs of black then don't sand the black spots ANY MORE! And it's best if you just get through the existing top colour and see the primer and stop then. If the existing paint and primer is already black then that makes it all the harder. In such a case I'd live with just giving the existing paint some scuff sanding and fill any small chips then paint. It won't remove the two or three ounces of paint that you would have taken off with a full removal of the old finish but it's better than risking sanding into the carbon layup.