Try a non aerosol sizing lube like Dillon's DCL or Hornady's One Shot. These lubes are lanolin based, cheap, easy to use and don't contaminate your loads. You also don't have so many problems with lube dents in the neck areas that typically occur with pad type lubes. STOS is not a sizing lube.
I used to use powdered graphite which worked well but left your hands really dirty until I discovered a product sold at MidwayUSA. I can't think of its name right now but it comes in a small plastic container like a short prescription bottle filled with plastic beads. You add some of the same company's powdered lubricant (graphite?) to the beads, shake it around a little and then dip your cases into the container. It puts an invisible coating of lubricant on the outside of the case and inside of the neck and works great!
The product name was bugging me so I just checked on MidwayUSA and they no longer offer that product. The same company - Imperial - now calls it a "wax" but it apparently works the same.
You can get lanolin at the drug store. A small tube (like toothpaste comes in is like $2.00.) Coat your finger tips and rub the case neck, so think tou cannot see it. Works good, does not contaminate the powder and makes your finger tips softer, just in case the Mrs. does not have a headache.
When i've had really big sizing jobs..like a 50 BMG fired in a automatic weapon.. I use tri-flo on my hands.. wipe everthing down.. deprime.. resize.. trim to length.. then tumble clean and load.. Never a problem..