@Madchatthew The general rule of thumb with Linux is that every kernel update attracts a reboot. The reason for this is that these updates cannot be affected with the kernel in use, so a reboot is the only way to ensure you have the best protection.
You cannot upgrade the Linux kernel without rebooting. At least not in a way you would think.
There are technologies like systemtap, dtrace, kpatch or kgraft which allow for small modifications of kernel code. These are meant as short “workarounds” to prevent security threats, and to typically to give you more time until you plan a maintenance window for reboot.
You will have to reboot at some point and should design your infrastructure for that (in the commercial sense).