Yes washing your hands is important when handling food for cooking but if the only water available is contaminated rinsing off with that water leaves your hands contaminated so the thing to do is to decontaminate the water. I have read about a doctor working in Africa that only had contaminated water so what he did was to use Potassium iodide in the saturated solution form, by adding ten to twenty drops to this water after about five minutes it was ready to drink.

Now this soulution of potassium iodide is also known as SSKI is probably can be obtained at a drug store, households today don't seem to keep this on hand as they did many years ago when it was known as tinture of iodine to use on scrapes and cuts.

So to sum up if you only have contaminated water to wash with if you had SSKI you could first treat it with SSKI before washing or for drinking.