There are daily nightly updates on CyanogenMod, and I have some waiting.
Can I just omit the older ones and update straight to the newest one?
Unless the maintainer of your device states otherwise, this can usually be done with no issues as long as it's the same version (CM13 to CM13, but not CM12.1 to CM13).
CyanogenMod's update system contains a script which "saves" Gapps from being overwritten, and writes a new /system partition, then clears caches, essentially just refreshing the core operating system... Basically the same way as doing it manually. Skipping is not only safe general, it is actually quite common as many people do not take well to the idea of flashing their phone daily. Many users often do it weekly or monthly, or just as they deem necessary.
You can always post in the official forum for your device and reference your current build and what you want to update to, if there is an issue the maintainer or other users will likely let you know.