Just download the new version and run it, you can even fully delete the old one. Your saves are stored in AppData, so they'll be untouched and automatically detected thereafter.
AppData is a hidden folder in your computer - Local Disk > Users > [your name]. Use the View tab when navigating folders to tick on or off hidden folder visibility.
If you've played (or specifically, modded and/or used texture packs) for Minecraft, this folder should be familiar :)
