Must the AxCrypt web services password be the same as the file access password?
You can set the software to be permanently offline. That way your encryption password is never sent to AxCrypt servers but you’ll lose access to the key-sharing function (which allows you to share files with other AxCrypt users) and also the AxCrypt password manager.
Both those features require a premium subscription so if you’re a free user then going online doesn’t offer you any benefit and you can safely use the software exclusively offline and your password will never be sent elsewhere. Free users are limited to 128-bit encryption.