"Blackmail" is the wrong word. Blackmail refers to the victim having done something in the past that they want to keep secret, and the blackmailer threatening to publicize what they have done if the victim does not comply with the blackmailer's instructions.
What Putin is doing here does not involve skeletons in our closet at risk of exposure. This is straightforward hostage situation where Putin is pointing a gun at our heads and threatening to pull the trigger if we move against him.
The ridiculous thing is, NATO also has guns, so there is no technical reason why Russia should have an advantage over NATO. The problem is that NATO values Russian lives more than Russia values NATO lives, and Putin knows this. This is why Putin thinks he can get away with anything. In order to stop Putin, NATO must learn to view Russian lives the same way Hitler did.