If you are able to run without a skimmer you probably should. BUT...
The obvious down side is that a reactor is expensive to run (consumable GFO and carbon) vs a skimmer...which virtually runs for free, forever. Some people reef with no mind toward budget, but if you do...there's a good reason so many folks have fit skimmers into their system.
- What made you add the skimmer in the first place?
- Also, can't you shut off your flow pumps separately from your sump return pump?
Flow Vs Filter Pumps
If you keep the skimmer, the "correct" solution for you during feeding is to leave the sump+skimmer running, but shut off your flow pumps in the tank. (And of course feed only as much in one sitting as makes sense so you aren't feeding the rocks and skimmer - and feed more frequently vs heavier to give your fish more chances to eat.)
It follows from your current process that you might be using your return as a flow source - if so, this is another aspect of your problem. Keep in mind that 2-4 times your display volume is all you need for sump flow in gallons per hour. E.g. a 90 gallon tank would be perfect with a return flow between 180 gph and 360 gph. More than that is overkill, and in your case (if true) it's actually causing a problem other than the usual noise and bubble issues.
Air Gap
One other thing to consider, which should really be in place no matter what your configuration/situation, is the air-gap for your drain plumbing.
If, when you shut off power, it's draining too much water into the sump, then all you need to do is cut/drill an air-gap higher (or to enlarge the existing one) so it works quicker at breaking the siphon from the tank. This way, the sump only has to catch the water that drains from the return plumbing itself (which should be mostly insignificant) - not additional water from the tank.