I could list many different reasons why this would fail, but I'll just name a few.
1) Of you Skill Swapper is taken out, you're left sitting dead in the water.
2) Shedinja doesn't have the firepower to take out a whole team before Struggling.
3) Burn, Poison and Confusion damage all bypass Sturdy.
4) Entry hazards.
This strategy has been tried — and failed — many times. Don't join them.