I sometimes wash wool sweaters on cold using the delicates cycle (I have shared washing machines in my apt. building so no fancy hand wash cycles or anything). I put them in a lingerie bag or pillowcase if I'm worried about something snagging. Generally it is fine. Felting and shrinking happen when you have the combination of heat and agitation, so if you use gentle cycle and cold water it should be fine. Although there are some fibers that will just shrink the first time you wash them (actually, cotton that is not preshrunk is the worst culprit); that's just the nature of the beast. But most wool should be fine.
<getting on soapbox now... you have been warned>
But PLEASE do not hang your sweaters to dry!!!!!! You need to dry them flat and block them into shape. You can pin them out on a towel if you want to block more severely. Hanging will stretch things out (like shoulders) that you really do not want to stretch, and causes undue stress on the fibers because they are heavy when wet. Silk in particular is extremely fragile when wet (although it is interestingly very strong when dry). It's OK to hang something light like a silk blouse to dry, but a silk knit should always be dried flat. Blocking is a much better way to get the length back where you want it without damaging the sweater.
I hand wash (or delicate machine wash) ALL my wool sweaters regardless of whether or not they say to dry clean. The exception would be if it had something like leather trim that you can't get wet. It's actually bad for wool to dry clean it, it weakens the fibers, plus dry cleaning chemicals are nasty.
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