You can see that some records are made with card board fillers, especially when there is a slight chip missing from the rim. But I've never had a problem with them swelling. Of course, I don't soak my records in water.

Here is a site that discusses shellac records from a professional preservation standpoint. There's also an image that shows a record with a paper fiber core:
https://psap.library.illinois.edu/collection-id-guide/phonodisc
By the way, the cleaning solution they promote should be used for vinyl only, not for shellac records.

The Library of Congress recommends cleaning the grooves with canned air:
http://www.loc.gov/preservation/care/record.html