Dawn is great for getting out oil and I have never had it stain my clothes blue. (I often use it as a booster to help clean my kids' really grubby clothes--they are in the "my tee is a napkin" stage.) I swear by it. However, I have had it bleach clothes when applied directly, so be sure to dilute it first.
For something like cashmere, I use Eucalan too. I have a gallon container. It is absolutely the best for preserving the softness of wool/cashmere. Dawn may strip off the oils that keep the fibers soft and pliable, dehydrating them. Dawn is the washing equivalent of using very inexpensive shampoo on your hair. Great if you have super oily hair, not so great if you have dry, fragile hair.
Unlike everyone else, I have had mixed results with washing cashmere. I knit, so I know the washing drill very well. Wash in tepid water (not too hot or too cold, or you shock the fibers, which causes felting and shrinkage), swoosh and squeeze, but do not agitate excessively (you cause the scales on the fiber to interlock, again resulting in felting and shrinkage), squeeze, don't twist to remove excess liquid (twisting will ruin the shape) and shape and air dry flat. However, I have had some mid-grade cashmere (Caslon from Nordstrom, I'm looking at you) shrink on me. Plus there are almost always small changes in the shape of the garment. Any areas with ribbing are the most likely to change. If a sweater was very expensive or it is a shape I absolutely do not want to change, then I dry clean.
Again, this is my experience, and I know others wash their sweaters routinely. I am very picky about the shape of my sweaters, so I probably am more bothered about it than most. Or another way to say it might be that my tolerances are much lower than most. So, if you don't mind a little change here or there in the shape of your sweater, it should be fine. If you do, then go cautiously. Also do a Google search on how to "block" your sweater to shape it and spend some time learning about that--it makes a huge difference.
