Well, think about this. You need to send the variable to the page--if they're not there, then they're not set. So, if you take them out, you've got no variables.
There are two things you could do. One's fairly similar and the other is a usable workaround.
The easiest would be to POST the data instead. This is practially invisible to the user (the browser sends the information without telling the user--unless you choose for it to tell you when you're POSTing data). This requires a form, and cannot be entered in manually.
The workaround allows you to still use GET. Check if the query string is not empty ([man]empty/man). If it isn't empty, just add a few session variables ($_SESSION). You can use [man]parse_str/man to get them into individual variables. Once the sesion variables are set (you'll probably want to clear the old ones), just redirect them back. For that, you use [man]header/man. There are examples on using 'Location:', but just remember that you must use a full URI, which you'll have to generate (don't worry, there's an example which shows you how). Then just work off the session variables as you would regular ones.
Hope you understood that. 🙂