How to change templates based on URL

Provided not showing the sidebar is the only difference you really want between the way pages are displayed, you can load the sidebar conditionally with something like this in your page.php (or whatever file your theme is using to load the page):

  if ( strpos($_SERVER['REQUEST_URI'],'/register') == false ) { // if requested uri DOESN'T contain '/register' load the sidebar.

That said, if you need farther reaching changes to the template for those pages, you’d be much better off making a new page template for those pages. Once you have a custom page template in place, you’ll be able to choose that template on the page edit for any page on the site. Instructions for custom page templates are in the codex.