Fix plaster behind skirting board
I understand not wanting to risk damaging that original trim, but it appears the piece is only a few inches long and not solidly attached. It's probably easiest to carefully remove it, use plaster and/or drywall to fill in the area behind, then reattach the short piece of trim.  If you damage it slightly, you can fill dents and cracks with wood putty, then just sand and paint.