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So if I have a 2x12 16 Ohm cab (assuming 2 x 8 Ohm speakers wired in series) then is it theoretically possible, and relatively easy, to add a switch on the back so that you can switch between series and parallel wiring so that it gives either a 4 or 16 Ohm impedence?

I think this is right, I just want to check my thinking with you guys...

Or if the cab has 2 identical inputs then can I just wire one to be 4 Ohm and one to be 16 Ohm?

Yup, the two inputs thing is surprisingly each actually.

Nice one ta.