I’m in the process of doing the same. I removed one of the lower stays for a couple of weeks while a new pair were made. The mast had a non-problematic, very slight curve to it, without the stay although I wouldn’t have sailed like that.
When it comes to removing the cap shrouds, back and forestay I’ll first loosen the opposing rigging, and tension a halyard in place of wire before removing the stay. The standing rigging is held in position at the end of the spreaders by a guide that is held in place with screws and/or a pin.
Our boat has rigging like you describe with a diagonal wire swaged onto the cap stays just below the spreader. The diagonal is thinner wire than the main stay and required careful measuring for its length and location on the capstay. Tensioning the diagonal is done using a bottle screw at the mast.