I have prewashed several jelly rolls - by hand. Just do a few at a time in the sink, squeeze excess water out with layers of toweling and iron. You might want to use an ironing surface with straight lines on it to line the strips up. This should work for charm squares (never done that) and could use the lines for squaring if the ironing surface is stretched correctly.
I prewash all my fabric by hand, use towels to soak up excess water, then iron. Yes, the fabric is wetter than other methods, but it makes it easier to 'straighten' up the fabric if it's off, and very few stringy threads.