What'd I'd recommend is copy-pasting over your "world" folder and your "moonbase_settings.json" files over from your old mewnbase game folder, to the new one. Run the new app, check that your save file loads/works... then delete the old version's folder. Hopefully that's pretty straightforward, but if not, feel free to ask for clarification.
For a more hassle-free updating experience ;) ... try out the Itch desktop app - it can auto updates games automatically without the need to manually download and transfer saves etc.
