There is no 100% safe way to introduce a new queen into a colony but this queen introduction will give your queen a better chance especially if you are re-queening due to the nature of your bees! If is quite acceptable to use the cage your queen comes in as the introduction cage but if you bad tempered bees they are likely to kill her at the earliest opportunity.
With this cage your queen has a better chance of being accepted. The cage is pressed into sealed brood on a frame that you have first shaken the bees off. The new queen is introduced into the cage which can be sealed with the cap or there is a fondant compartment that can be used - if using a fondant plug you need to be sure the brood will emerge before the worker bees outside the cage have eaten through the fondant.
having put your queen into the cage she is on her own with the sealed brood. As the young bees emerge they will immediately accept the queen as they know no difference. After plenty of young bees have emerged, which may take a few days the cap, if used, can be removed so that the queen can escape in her own time, do not to this too early. The cage can then be removed once the queen has left.
Ensure you leave enough space for the bees to be able to feed the queen through the cage.