So instead of a submit button, the user is just clicking a link? If so, you can use javascript to submit hidden form elements. Not exactly sure how to do it, but I know it's really easy.
Just reread your post. I'm not sure if you would consider this submitting a form.
This could possibly work:
$_POST['myvar'] = "astring";
Then on the next page:
$myvar = $_POST['myvar'];
That seems too simple though, so it doesn't seem like it would work.