Pact of the Blade states:
You are proficient with [your pact weapon] while you wield it.
If your PW is a shortsword (or any other non-simple weapon), and you are wielding a regular shortsword in your off-hand, do you get to add your proficiency bonus to your off-hand attack?
My guess is no, that you're only proficient with the actual PW, and not any other weapon, even if it's exactly the same 'type.' But it's still a bit... odd.