Brian, If you can find a store that sellls Japanese carpentry tools, there are several very lightweight saws that they use. I have a small folding saw that is very light and the blade is razor sharp. The blade is very thin, so you have to be careful with it, but it would cut anything you would want for a shelter.

I dug a trench shelter last winter, not because of an emergency, but because the weather was really clear and I didn't feel like putting up my tent. Didn't take long. I didn't even need a cover over it. If I had, I could have made one, I suppose.