If you're on Android, just install the new apk on top of the old one. Otherwise, just extract the update to a fresh folder and play (the saves will be transferred automatically and you can delete your old folder any time) :)
You don't HAVE to delete the older version if you want to keep it for some reason, but you can, yes, and it won't screw up your saves. You can even delete the old version before downloading the new one - the saves will still persist :)
