Because I've not made the Evernote application I'm not able to edit the Evernote keychain.
So I use a very big workaround to get this done: the clipboard. I know a bit dodgy but it gets the job done.
Your Evernote password is stored encrypted and is only decrypted upon switching. Your password is then copied to the clipboard, pasted into the Evernote login window and then the clipboard is emptied.
Because of this work around access to assistive devices need to be enabled. Evernote Account Switcher will enable this for but it needs your permission to do so. It means it will ask for your password.