Can I install it like an update for CM or do I need full wipe / factory reset?
My 7.1.13 ROM seems to shut down after some time without any notification, so it's turned off and I assume it being turned on.
It's not a full ROM, so if you were to do a full wipe before flashing, you would end up with a bricked phone.
When flashing different kernels, there usually should be no need to wipe anything, which is especially true in this case when there is just one tiny detail different....
Just flash and reboot - it will work fine