How to change what ssh:// uses?

You can use a tool that is very comfortable to change the default app for specific URL handlers.

Change the ssh URL scheme with RCDefaultApp

1. Download RCDefaultApp Version 2.1
2. Install the Preference Pane
3. Go to System Preferences > Defaults Apps > URLs
4. Go to "ssh"
5. On the right side, select your preferred application

It will look very similar to this screenshot:

To answer your question about changing the ssh:// protocol client,

Per https://superuser.com/a/548122/202319 , you can modify ~/Library/Preferences/com.apple.LaunchServices/com.apple.launchservices.secure.plist to open any app with a registered identifier when ssh:// or another URL is encountered.

This is not a perfect solution, because it still requires an app bundle, or will use Terminal.app (which is what you see already).

But, you should be able to fix your .login or .bashrc files so the default Terminal.app shell would use your preferred ssh anyway.