Reply #7543 says that “In the future you’ll be able to download a license file containing this information directly from the web or from the app, and import it directly to the app.”
You’ll have to wait until AxCrypt implement this for you. Franz’s method would work but if you’re not comfortable changing the source code then you’re out of luck.
I fully understand your concerns about sending your password to a blackbox server. I take an educated guess here but I suspect the majority of AxCrypt’s customers never use the Key Sharing feature so there’s little need for the password to be submitted to the server, apart from receiving the private key and even that could be delivered without needing a password.
You might look at VeraCrypt but that’s a volume encryption product, AxCrypt encrypts individual fiiles. You’d have to upload sparse bundles to your cloud and this is not suitable if you regularly update small, individual files as you’d be wasting much bandwidth.
Until/if AxCrypt allow you to import a license file using the free AES-128 is better than nothing.