If they were frozen stiff, and not preserved prior to freezing, the cells are probably completely burst and it's just proteins holding the tissue in the form that it is. It's probably swollen because the cells that would normally be functioning to move fluids and ions around are dead and it's just pooling.
If you could get some VERY sharp scissors to cleanly cut off the tissue that is dead/filled with fluid, that would probably be best. Surgical scissors would really be the best if you can get them. Else, you'd have to just wait for it to turn black and fall off, but that comes with the pain and a greater risk of infection.
I'd cut them to the contour of his chin so to say. Don't pull and cut as that might get more than wattle.