I've never seen a deadbolt lock where installing it on either a right-hung or a left-hung door depended on removing the lock cylinder.
A deadbolt lock has three main sections: the outdoor part (which contains the lock cylinder), the indoor part (which has a knob for throwing the bolt), and the deadbolt mechanism.
Remove the screws that hold the indoor part and the outdoor part together. Now slide the indoor part and the outdoor part away from the deadbolt mechanism. Put the indoor part where the outdoor part was, and the outdoor part where the indoor part was. Put the screws back in.
Done.