I want to replace the 17" Crown Spoke rims my mini (2008 R56S) is wearing, with new ones. What specs should the new rims have, so that they will fit in without issues?
So you are going to cut off the rims? That's going to be a mess. Just get new wheels! And it is a pet peeve of mine.
Get a set of stoner rims. You know, like the kind the Flintstones used... They'll never fail you and I'm sure there's plenty of stone in your neck of the woods to suit your need.
Try "Tire Rack" they have a ton of info. https://www.tirerack.com/content/tirerack/desktop/en/homepage.html