WARNING: This exercise has been performed by experienced stunt sysadmins. Do not try this at home without professional supervision.
You will need to manually download a few packages from the repository. A full local mirror of the repository might make things a little easier, but it's not required. I use lftp or lftpget with these paths conveniently bookmarked:
ftp://mirrors.us.kernel.org/fedora/updates/10/x86_64/ ftp://mirrors.us.kernel.org/fedora/releases/10/Everything/x86_64/os/Packages/
Always check the updates directory first for the latest version of the rpm, or you might end up with incompatible dependencies.
Enough talking, now let's roll:
rpm -U --ignorearch kernel-2.6.27.15-170.2.24.fc10.x86_64.rpm
rpm -i --ignorearch --force glibc-2.9-3.x86_64.rpm glibc-common-2.9-3.x86_64.rpm glibc-2.9-3.i686.rpm
rpm -U --force --ignorearch rpm-* libz-* ...
rpm -i `rpm -qa | sed -ne 's/i[36]86/x86_64.rpm/p'`
Good luck!
If something goes wrong and you're stuck with an unworkable, you could boot off a 64bit live CD and manually copy the files you need or chroot into your half-upgraded system.
You might need to unpack rpms with rpm2cpio. Also note a few rpm options useful in
recovery scenarios: root, justdb, rebuilddb.
If you manage to break your system in interesting ways, I'd like to know (but not necessarily help you fix it).
Please, edit this page with additional notes and tips. It's a wiki for a reason.