first you have to think about why you make splits. 1. to increase your hives. in this case, you have no virgin so your choice is to let them make their own, or to buy a queen. 2. you think the hive is going to swarm. here you take the mature queen away so that the hive believes it has swarmed. you leave the swarm cells behind so that the hive can requeen.
you might also split a large aggressive hive. in that case, you might kill the queen and allow both to requeen...or you could purchase queens.
if you make a split and the queen in the hive is a virgin, the hive has likely already swarmed and has no resources to make a new queen. if you are raising queen, you could have virgin queens for your split if you caged them before they hatched.
if you have queen cells and you want to requeen a hive, you can kill the old queen and use the cells in the hive.