most coaster brake arms can be removed from the hub. Take the wheel off the bike and look at the brake arm. there will be a nut on the outside of the brake arm. take that nut off and the arm will slide off of the axle. the brake arm hole will have a flat spot in it, which is used to locate it to the axle. you will have to hold the other side of the axle tight to loosen the brake arm nut. screw one of your axle nuts onto the axle on the sprocket side and hold it with a wrench while you loosen the brake arm nut. do not hold the axle itself with vise grips or channel locks because you will damage the threads.
take the brake arm off, put your new sprocket on (you may have to remove the dust cover because the sprocket hole may not be large enough to fit over the dust cover). after you get the sprocket on, then just slide the brake arm back onto the axle, and put the nut on tight. you will have to check the clearance between the sprocket bolt heads and the brake arm...the bolt heads might rub on the brake arm. you can slightly bend the brake arm for it to clear the bolts if you have to. make sure that the brake arm will still mount to the frame similarly as to how it came off. i am not familiar with the cranbrrok, so i am not sure if it has a mount welded to the frame for the brake arm or if it just uses a metal strap.
it's not that difficult to do, but you must be able to understand how it will all come together and you must be prepared and able to make adjustments to make it all work.