Airlock Issues in Primary Fermentation

Can it do the champagne corks that look like a mushroom?

I’ve corked Belgian-style bottles just fine with it. Mine is the wine version, so you need to make a spacer plate for the bottom or raise the handle, drop the support, and re-compress the cork to “push” it out of the corker. Haven’t tried it specifically with champagne bottles/corks, but there is a champagne version of it and I’m sure it’s just as nice of a machine.

Can anyone tell me exactly what type and # of cork I need for standard champagne bottles? I am having trouble finding them online. Thanks!