Anybody know how to repair this?

A Ewarts tap with reserve that I managed to knacker while trying to work out how to replace the cork.

Is the head to shaft connection a square pin and how would one separate the 2 correctly (ie not the way I did)? There must be some way to replace the cork (anyone know where I can get corks?)

For some reason I also have another plunger, still intact, so I can work out the correct orientation to reattach the two parts if a solution can be found.

Cork is 10mm x 9mm with the shaft being 4mm.

Thanks
Cack-handed Pete