Are there any piers in the single skin wall?
Look on the Trada website as they provide details (free) for timber constructions. My first pass is yes, insulated timber stud should be fine, but it’s the interfaces which may complicate matters.
Edit, if you are going to be fixing kitchen units to this wall, consider jumbo stud, effectively regular stud with a skin of plywood to provide additional strength and you can fix what you like, where you like.