What exactly do you want? If you want an exact replica then no, you can't use a Mk1 barrel. If you just want a lightened short barrel, then you can use a Mk1 barrel as per the Indian Mk1/3 gun barrel which used a shortened lightened Mk1 barrel. On the other hand, if you just want a couple of spare barrels to shoot the shxx out of, then just use a couple of standard barrels anyway

If you want an exact (?) replica of the barrel on the gun now, then you've got to use a certain type of Mk2 barrel that are in plentiful supply. Your Mk3 gun shortened barrel was developed from the Mk2 gun barrel

Machining down to length and diameter is a piece of pudding