For the first tree I would leave it alone for awhile to see if it might push some more leaves higher up. In the end for this tree and the second, cut off any black branches; but cut back to the first green bud. If you leave some of the black or dead branches, they will continue to die back.

In the first picture two of the new shoots are from the root stock, the ones with the trifoliate leaves, the third one is from the scion which needs to be kept and grown on into a new tree. There is no rush to cut back the tree in the top picture. You have PLENTY of time to do any cutting back. I would recommend you wait and insure no new growth will occur. You will be surprised how quickly the scion shoot will develop back into a new tree. Remove the trifoliate shoots from the top pictured tree. In the second picture do as Johnmerr suggested.

Thank you both!