All the above are IMHO good ideas and I think the knife shown is a good choice. Slip a few band-aides into the package.

Try to remain calm when they cut themselves. I know it is hard for parents to see a kid in pain and resist the urge to freak out and keep them away from dangerous items like knives. But, IMHO, the more constructive response is to calm them down and reassure them that you know it hurts but it isn't going to hurt for long. That it is okay, and they will heal. Then escort them to the bathroom, instruct them on how to wash their hands and clean the wound, how to gently dry the cut with tissue so you don't get blood on the towels, and how to apply a band-aide. Let them do the job even if it isn't done exactly right. If the bandage falls off after a while it is good practice in field dressings.

I respect parents who can emphasize that getting hurt a little bit is normal, that the pain tells them that they are healthy and haven't severed nerves, that bleeding is a way for the body to wash away dirt, it is good. That they are strong, healthy, and smart and there is every expectation that they are going to handle small cuts on their own after a little practice. That making a mistake and slipping with the knife hurts but it isn't wrong, they aren't bad for making a mistake, you aren't mad at them, and they will do better next time. All this while being reassuring, and remaining calm.

That is a tall order for a parent. But if you do the best you can, and accept your own faults, the kids will be inclined to do the same. Both with you, and with themselves.