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[africancichlidau]

I wouldn't be too persistant in trying to remove the rest of the old skin if it is just a small piece or two and only around the wound scabs. The skin may in fact be seperated from the new but being held on by the scabs and removing it could open up the wounds again. Once the scabs heal it might be a different story but the old skin will probably come away in the healing process. Very difficult to say without seeing the animal but it is something worth checking closely in my opinion. That is all it is mind, my opinion.
Good luck with it