I'm not sure I perfectly understand your situation, but as far as using
ssh-keygen, you don't want to use that because users will need to login to the cluster computers from, say, a public or home machine where storing the key isn't feasible/secure? Otherwise, it would be quite easy to do that.
Unfortunately, I cannot think of any easy one-liner way to supply a password to ssh, and the best info I found on line was this:
http://nixcraft.com/shell-scripting/4489-ssh-passing-unix-login-passwords-through-shell-scripts.html. It's a bit of work, but it could do what you want. If you want to implement that and need any help, just let us know.
On the other hand, would it really be so bad to have a shell pop up and prompt for a password?