I see all the instructions on line for replacing cork. However the cork on my old 3 piece alto recorder is not on the outside, but inside the mouthpiece and inside the bottom piece. It will be difficult replacing it smoothly. Is there any reason I cannot clean out the cork and then replace it on the outside of the tenon?
I think it would be possible to do what you suggest. After getting rid of all that old crud, I think I might try to use thread instead of cork, but whatever is easier, I guess. Take a look at the documents on this page
for some guidance (shows how to use thread and cork, etc.