How to safely remove this old hot water radiator?
With the boiler removed, if there is any water it will be minimal and not under pressure. Have some towels handy unless you want to go to the bother of figuring out where to connect an air hose or shop vacuum to the presumably disconnected pipes where the boiler used to be. And then have some towels handy anyway, but either of those will help get some of the remaining water out, if there is any. 

You'd expect possibly some dirty and/or rusty water if the system has not dried out since it was disconnected. They often don't dry all the way out, as water ends up trapped somewhere.

Cutting the pipes should be fine.