I would not, instead I would use other simple remedies instead before that.
For skin healing problems, even though as a person ages, the skin becomes thinner, that is normal age related changes. Has the person tried wearing long sleeve shirts to protect as much skin areas as possible. Even though some diesease processes can affect the healin of the skin, ie diabetes, possibly AIDS (as mentioned in the next line), those are issues easily corrected by changing the types of clothing being worn, and will help protect.
The AIDS issue is a bit more comlicated, because of the potential to transfer the disease. I have not heard of a cat being a carrier for AIDS in the past, but that does not mean to say they cant. Maybe others on the forums can supply a better answer to this one than I.
As for the cat attacking small children, there could be a lot of reasons for this. Overstimulation for the cat, heridity, an abusive past? Also look at how the children are interacting with the cat, and if the cat feels threatened. Does the cat have scratching posts? Is there play time for the cat only? Are the kids pulling on the cats tail? Or patting or rubbing the cat inappropriately? Does the cat get enough stimulation? Lots of reasons for this, so it might be advantagous to look at the reasons the cat is attacking young small children. The cat might feel that they are not the centre of attention and is looking for attn too. Who knows. this also kinda addresses the fourth issue as well.
Behavioural issues for the most part be corrected with positive stimulation for the cat over a period of time. USe of treats for good behaviour is a good way to help reinforce the proper behaviour. I was taking my first cat out for walks, and she did not like the harness, and for the first while I put it on her, she would just lay on the ground, but after awhile (when she got used to it) she would go for a little walk outside, then when we got home, I would give her a treat for going outside and enjoying the day. This same cat attacked a dog I look after as well, and when I saw her do this, I put her in the bedroom with her food and water dishes, and closed the door and left her there for a period of time. After a while I would let her out, and if she did it again, I would do the same thing. After a few days, she got the message and accepted the dog. She did not interact much with the dog, but she was not attacking it either. Cats can be trained, you just need patience and time. Best of luck. There is my 2 cents on what you asked. If anything, do not put hte cat down, that is not the best option. Maybe try finding a different home for hte cat woudl be a better option. Just my opinion.