If you don’t plan on having it save passwords, you can add the following to the .desktop file your using for the Exec line:

–password-store=basic

The line for my chrome setup for some public computers at work is:

Exec=/usr/bin/google-chrome-stable --password-store=basic %U

So you’d just need to replace the file path to your chromium path and it should work.

It’s been a long road…