This depends on a combination of factors: What are you charged (call it margin interest) to hold the position? How does this reduce your buying power and what are the opportunity costs? What are the transaction costs alternative ways to close the position? What are your risks (exposure while legging out) for alternative ways to close? Finally, where is the asset closing relative to the strike?
Generally, If asset price is below the put strike then the call expires worthless and you need to exercise the put. If asset is above the call strike then put expires worthless and you'll likely get assigned.
Given this framework:
If margin interest is eating up your profit faster than you're earning theta (a convenient way to represent the time value) then you have some urgency and you need to exit that position before expiry. I would not exit the stock until the call is covered. Keep minimal risk at all times.
If you are limited by the position's impact on your buying power and probable value of available opportunities is greater than the time decay you're earning then once again, you have some urgency about closing instead of unwinding at expiry. Same as above. Cover that call, before you ditch your hedge in the long stock.
Playing the tradeoff game of expiration/exercise cost against open market transactions is tough. You need sub-penny commissions on stock (and I would say a lot of leverage) and most importantly you need options charges much lower than IB to make that kind of trading work. IB is the cheapest in the retail brokerage game, but those commissions aren't even close to what the traders are getting who are more than likely on the other side of your options trades.