According to information freely available in the links provided to you, no, as a general rule of thumb, the exploits will not work on the slim-line PS2. Oh, and ironically enough, you need either an AR or the Swap Magic disks to even do the exploit. Or a USB Flash Drive. Maybe an original PSX disk. And possibly a PS2 HDD.
Good luck.
EDIT: You're not old enough for Paypal? Do you have a bank account? If you do, then age doesn't factor into it, as far as I know...
