Interactive Brokers (here, here) is not allowing exercise if you don’t own the stock because there is no inventory (here, here, here, here).
Well back in CCME I had a few shares long when it got halted but also had more put contracts at the same time. I exercised all my puts and it was absolutely no problem to go short on the stock that way during the halt. And mind you CCME was one of the most shorted china stocks of all times back then. IB is really good in these things.