Razor wire is called that because it looks like a razor.

The danger is about the pointy shape.

I'd be careful climbing it, if you fall/slip it's way worse than barbed wire. (Not sure how to do it tactically)

I don't think it's that unethical to put it around the cat if it's obvious. It might be a danger in an accident or something.

https://en.m.wikipedia.org/wiki/Razor_wire