Your insight suggests an even better solution: the spacewalking astronaut could open the internal hatch to the docked Lunar Module so its cabin air can instantly partially repressurize the Command Module
Maybe, IF the hatch can be opened when there is a pressure difference. It might be dangerous or even mechanically locked out in those cases. It may not, I have no idea.
I mean we're just guessing and spitballing here, and all of this assumes that whatever incapacitated the CMP is fixable by the other astronaut. But it does look like there may be a decent chance the CMP could survive this. Of course, he might have internal injuries or they might not be able to restart his heart. But seems like this procedure would be worth a try.
Opening the hatch was a huge pain. They'd have to disassemble the rather phallic docking mechanism (as Collins described it). Not being able to disassemble it was one of the fears Collins had about Apollo 11.
I mean we're just guessing and spitballing here, and all of this assumes that whatever incapacitated the CMP is fixable by the other astronaut. But it does look like there may be a decent chance the CMP could survive this. Of course, he might have internal injuries or they might not be able to restart his heart. But seems like this procedure would be worth a try.