No. You're correct about how you characterize the minister's decision. After the committal, if there's a committal at the extradition hearing, it goes to the minister. The minister then makes the decision about whether to order surrender, and it's the surrender order that will allow the person to be transferred to the foreign country making the request.
The withdrawal of the ATP is relevant only before the decision of the extradition judge. Once the extradition judge has ordered surrender, the ATP is used. It has been decided upon.
The withdrawal of the ATP is also delegated to officials, and that power exists in case something changes between the time the authority to proceed is issued and the time the extradition judge makes a decision on whether to order committal.
For example, if the extradition partner withdrew their request after the proceedings had commenced, we could withdraw the authority to proceed and recognize that there was no longer a basis...or if something happened to the evidence that we had reviewed in order to issue the authority to proceed, and we no longer had confidence that there was sufficient evidence to justify a committal, we could withdraw the authority to proceed. That action is taken by officials in my department, in the international assistance group; it's not taken by the minister.