Definitely, I would leave the skimmer running. I don't know if you could get this done in the time you have, but here is my solution:
My skimmer is an in-sump.
Skimmer cup drains into a 2 gallon waste bucket I keep next to the sump (my sump is elevated).
In the waste bucket there is a water level sensor and switch.
When the water level in the waste bucket rises too high, it turns off the skimmer (it actually turns off the electrical outlet the skimmer is plugged into).
The skimmer stays off until the waste bucket is emptied and the level switch is reset.
I normally skim wet, but if I'm leaving for a few days I turn it down to skim more dry. Generally, it would take a month or more to fill the waste bucket anyway. If I set the skimmer to produce drier skimmate, I can easily double that interval.
The level switch is just insurance in case the skimmer does go nuts for some reason (which it has a few times).
This is easy to set up with almost any modern aquarium controller system, but the setup for my skimmer is self-contained, and would work without any controller system.
If you had to do this, just connecting the drain hose to the skimmer cup and letting the skimmate drain back into the sump should be OK for a week. It would be much better than turning the skimmer off.