confirmed on Catalina as well! - can you please post here when it's fixed? I would love to try it!
The version currently available at https://www.fatpick.com/downloads/FATpick-mac-latest.dmg is fully notarized by Apple and should not have this problem.
Release notes here: https://www.fatpick.com/blog/release-notes-fatpick-v1-4-2
Please let me know if you encounter any problems with this new build. You can reach me via the contact form at https://www.fatpick.com/contact-us or you can email me directly at rod@<that-domain>.
In the meantime you can make an explicit exception by "right-clicking" on the application icon and selecting "Open" from the context menu that pops up.