Tag Heuer Pusher Removal/Replacement

[Tifosi100]

Hello - I have Tag Heuer F1 Chronograph ca1212-ro, which I've had for many, many years.  Recently I noticed a pusher "cap" had come off and was lost, I have sourced an new pusher, and have removed the movement but am at a loss for how to remove the pusher from the case???  The new pusher is not threaded so I'm assuming the old one is not either - assuming the pusher I was sold is correct.  Are the pushers a o-ring press fit, are they "glued" in, how are they removed and reinstalled?  Any help is greatly appreciated!  Thanks - Nick

[Hermann]

I would try only to migrate the cap , screwing from inside. Let me know if the cap fits the original pusher guide