sessions will not hide the parameters, they just let you store parameters on the serverside, so you only have to send the altered data through GET.
POST without a form is possible (anything is possible) but waaaaaay more trouble than it is worth.
A hidden frame is probably the easiest solution.
Another method is to not hide the parameters at all, but make them look nicer.
Apache/PHP have the ability to take parameter as virtual directories, so this:
http://www.foo.bar/idnex.php?foo=these&bar=are&foobar=parameters
turns into this:
http://www.foo.bar/these/are/parameters
but you loose the keys, so you have to know the order of the parameters and the order may not change.