Some have a hex socket, some don't .... which is unhelpful. Yes, if you resort to the angle grinder, you'll need a new lower wishbone. Heat will destroy the rubber joint cover, but you can get new ones of these.
1) All of the manuals suggest simply loosening the nut, then doing the joint split - because the nut stops the joint completely flying apart when it gives. Unfortunately, you end up with your problem....
2) So - put a bottle jack under the ball joint, with a bit of wood to protect the joint - then drive the joint back together again.
3) With the joint firmly back together, you may have enough friction to undo the nut. If not, then tighten the nut so the joint is fully back together - you will certainly have enough friction now. Make sure the thread is lubricated - rust is probably what is making this happen.