I know that iCloud Keychain has a feature where it offers to generate strong, random passwords directly in Safari. Some third-party password managers allow it, but I'd prefer to store the password in the OS X keychain, so I'm really just looking for a password generator, not full-blown manager. For other browsers there is addons that offer similar functionality. It's possible to do it in the regular non-iCloud Keychain Access app, but this is a bit cumbersome.
Is there any way of generating a random password directly in Safari, but without using iCloud keychain?