My problem is that newer version of putty store the keys in the registry and the registry entry is not in ppk format. There does not appear to be a .ppk file on my disk.
No, it has nothing to do with newer PuTTY versions – rather, you are confusing two different kinds of keys.
Just because you don't have a .ppk file doesn't automatically mean that it now goes to the registry; it could just as well mean that you've never had a key in the first place. User keys are not automatically generated by PuTTY – creating them is a manual process of 1) using PuTTYgen and 2) uploading the public part of the key to the specific server.
If you've been using a password to connect the SSH server, then most likely you do not have a private key that would go in a .ppk file yet.
What you found in the registry is a different thing both in content and in purpose. It's the PuTTY equivalent of what OpenSSH would keep in the known_hosts file, i.e. it is not your private key but rather a public key representing the server (as every SSH server also has its own key, much like SSL certificates). Such entries cannot be converted to .ppk files because they have no corresponding private key, nor would it make any sense for you to have a .ppk of the server anyway.
So you should either a) generate a SSH key for yourself (and make sure to add it to the server's authorized_keys), or b) carry on with using a password, without specifying a .ppk file at all.