I successfully changed from a google sign-in to an Airdroid password. The way I did this was to go to the account settings on the website and add a password.
The password page initially showed no current password. I entered my new password and tried to change it, but it complained that it wanted me to enter my current password. I entered the current password on my google account and it accepted that.
When I did that, I got an email warning that the account had been signed out. The device also had a similar warning. I signed in again on the device using the email address and new password and that worked. I then fired up the desktop app, signed in with my email and the new password, and it connected.
I then fired up the desktop app, for which there is no way to sign in with a google account, and signed in with the assigned email address and the new password. The app signed in successfully.