CWP Secure Kernel is a regular linux kernel with a security addon. The security addon is Tomoyo:
https://tomoyo.sourceforge.net/The linux kernel doesn't include the security addon Tomoyo by default. The kernel must be recompiled with the Tomoyo enabled. That is why the security enhancements don't start when you boot the server using the update kernel.
However, I think CWP Secure Kernel should protect your from such vulnerabilities. It should not allow to run suspicious executable files/binaries, etc. Anyway, it is better to get confirmation from CWP Secure Kernel developers or check the Tomoyo rules if you understand Tomoyo )