Check if there is already a valid one-time-password -reset link
In D7 one-time reset pw links are generated using the normal hashing techniques (plus a timestamp) but they are not saved in the DB (see  user_pass_reset_url). This means that there is no way to resend a link (without doing some major work to store this on your own). I don't see why you would care about resending the identical link, but I'm sure you have your reasons. 

If they do click a reset password link, I would recommend that you style the password reset page using a completely different page template that does not include your navigation links (etc...) rather than trying to disable them. Just be sure to add a message with a link to the homepage (or where ever) once they successfully edit their password, or even better, do a redirect upon success.