I think turnstep's FORM method is the way to go. The browser will probably dump any POST data if you do a redirect (I'm sure of it). The only possible solution I can come up with is writing some sort of proxying server in the first script, in which case you're back to using LWP as btrott suggested.

There may be a JavaScript way to avoid displaying the form and the Action button for the user, but that's beyond the realm of this lowly Perl Monk.