Securing Debian Manual: 4.2.2 Security update of the kernel

[Stayvoid <stayvoid@gmail.com>]

Hello.

"If you are doing a security update which includes the kernel image
you need to reboot the system in order for the security update to be
useful." [1]
How to make it on a running server?
I don't want to disable my site and mail for that period of time.
Should I use another server to keep them running?

http://www.debian-administration.org/?article=70
Will it work with GRUB?

"* When the new system comes up the second time, disable the 'support'
account."
How to disable it?

[1] http://www.debian.org/doc/manuals/securing-debian-howto/ch4.en.html

Cheers