Pusher for vintage Heuer Carrera 2447S

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Recently I purchased a vintage Heuer Carrera 2447S, which was missing crown and one pusher cap.
Crown is found. Now I only need to find a correct pusher.
I am not sure about the measurements. When I tried to measure the one that is still present, it was around 4.4mm / 2.7mm.

Thank you for the space and any advice!