Hi, and welcome to LQ!
And I'm afraid that this won't work, unless your hoster also gives you
at least shell-access via a serial console or networked KVM.
If repartitioning on the fly was possible for centos you could conceivably
slap a pre-installed slack-setup into the free space, modify the boot
loader within centos to see the slack-partition as well, and then reboot
(with a little luck that will work) into it. Do they have someone there on
site who can do manual stuff if required?