I guess it's ordered by now so, since you are going to be doing quite a lot of sanding, you may want a bench peg as well.  It holds the clarinet between your belly and the bench and makes sanding the corks quite a bit easier and quicker.

Be careful not to sand the wood of the tenon.  That leads to wobbly joints.

Yamaha 26s are always 3/64” or under though. The only way the cork would need to be thicker is if someone shaved the plastic down, in which case OP should probably have the tenon replaced as now that would be a weak spot. But that’s a very unlikely situation.

If you have problems getting the right thickness I would highly recommend a good set of calipers. You can wrap the cork around the tenon and compress it a bit with the calipers to get a good estimate of what the compressed diameter will be. Using this method I’ve never had to replace a cork because I used the wrong size.

Thank you Dave! Would the same apply to a wooden instrument? Meaning did Marlene also make wood alto clarinets or just hard rubber?

You see those cases every now and again. Somebody with too much time and money in the 70s wanted to get into the groovy aesthetic of the times.

I'll order the next size up, 1/16" thick instead of the 3/64 as mentioned above.
Cheers!

Why? That's just a waste of time and money...