Impurity of a severed limb for a Cohen

If a Cohen has had his finger severed, is he allowed to take the finger with him?

If the finger is without bone, flesh, and tendons, it does not cause impurity of a dead body. If the finger is whole and it is possible to reattach the finger to its place, it does not cause impurity, and it is permitted to take the finger with him. However, if it is impossible to reattach the finger to its place, a limb from a living being causes the impurity of a dead body, even though this is his own limb.

Shulchan Aruch Yoreh Deah Laws of Mourning, Chapter 369, Paragraph 1: 'The Cohen is warned not to become impure by contact with a corpse, as well as by contact with all the impurities that emanate from it, and not by contact with a tomb and a tombstone, and not with a limb from a living being that does not have enough flesh for the limb to heal if it was connected.'
And the Pitchei Teshuva wrote in Yoreh Deah, Chapter 369, Subsection 3: 'See (in Responsa Noda B'Yehuda, Tinyana, Chidushei Yoreh Deah, Chapter 209) who wrote that a Cohen whose legs were cut off and they have flesh in a way that they cause impurity, it is obvious that it is forbidden for the Cohen to hold them with him in order to show what was done to him so that they will have mercy on him, for he is warned even against becoming impure by contact with his own limb, see there. And see in the book Har Eival, beginning of Branch 18. He writes: ”if it is not a whole limb, he is allowed to touch it and the prohibition of half-measure does not apply here. Since there is no whole limb, no impurity applies to it, see there.'
And even though the Taz (Turei Zahav) holds that when the door is hanging on its hinges it does not interrupt the spread of impurity, his words have already been rejected in Nekudat Hakesef.