Is it possible to let Picasa use a removable device as the Application Support folder using symbolic links?
Whilst I have no experience with Picasa, I have symlinked many other apps' Application Support folders to other destinations including network drives too without any problems. I ensure the drive is connected with a script before allowing the app to open, but I'm not sure if that's necessary. Generally speaking, it'll work fine.

┌── ln(1) link, ln -- make links
│   ┌── Create a symbolic link.
│   │                                      ┌── the path to the new folder
│   │                                    ┌─┴────────────────┐
ln -s ~/Library/Application\ Support/App /Volumes/MyDrive/App
      └────────────┬───────────────────┘
                   └── the path to the original file/folder
                       can use . or ~ or other relative paths


Edited from my canonical linking answer at How can I create a symbolic link in Terminal?