Hello, my name isXXXXX and I have over 20 years of experience as a veterinarian.
I understand that your kitty Harry has a rubbery, horn shaped skin growth on his neck.
I think what your kitty has is a a mass called a keratin horn.
If so they are not a common mass found in cats, but they do happen.It is a proliferation of the cells of the hair follicle cells, in this case the cells that form the outer portion of the hair, growing in an abnormal fashion.
I do recommend that they be removed as they tend to catch and the top break off which can lead to the base getting secondarily infected. If the base isn't removed completely it will likely come back.Ideally removal would be removed via surgical excision.
I wouldn't anesthetize him for that alone but if he needs something else done such as cleaning his teeth that would be a perfect time to completely remove it. Or is he's a very coperative fellow they could use a local anesthetic and remove it. The base is usually quite narrow and it should only need a stitch or two to clsoe once removed.
Best of luck with Harry, please let me know if you have any further questions.