How could you distinguish between an irreversible electron transfer couple and a chemically irreversible couple using cyclic voltammetry?
To this question there are black-and-white as well as grey answer parts.

Chemical reversibility refers to the generation of a species that cannot be reduced or oxidised furthermore. In case you scan at moderate speed (scan rate), you may reduce or oxidise a compound and this intermediate can further react to an electrochemically inert species. If the follow-up reaction occurs fast, this couple is chemically irreversible.

Electrochemical reversibility refers to the rate constant of electron transfer. High rate constants (fast electron transfer) are found in electrochemically reversible couples whereas low rate constants are found in electrochemically irreversible cases.

Okay, you can trick chemical reversibility by scanning so fast, that you oxidise/reduce the intermediate of a redox-reaction at the electrode so fast that it has no time to further react. In this case, you should have only a forward-peak using slow cyclic voltammetry without a backward-peak; but you should start to see a backward-peak as you increase the scan rate.

For electrochemical reversibility, you can use Butler-Volmer kinetics. The main message of Butler-Volmer is that you increase the rate of electron transfer by increasing the potential. Electrochemical reversibility is seen on the peak separation between oxidation and reduction peak. Reversible systems show a peak separation at standard conditions with one electron transferred of 59 mV.

So, how would I dinstinguish them using cyclic voltammetry? By the peak shape and the change of CV by varying the potentials and scan rate.