I've washed pretty well everything that was dry clean only with no bad results, and handle and wash raw wool and handspun all the time - again with no problems. I'd use lukewarm water and the rinsing water must be the same temperature as the water you washed it in. Wool shrinks if exposed to changes in temperature - especially hot to cold. So keep the temperatures even. It also felts/shrinks with agitation or the combination of agitation and detergents/heat/temp changes - so I'd tend to just dunk it, let the fibres soak rather than swoosh it round much, and lift it out bearing its entire weight, between washing and rinsing.
I have done this with things with interfacing - I suspect success depends on the quality of the interfacing and whether it was cheap, adhesive backed or something hand tailored and sewn/tacked in... But then I think the chemicals in dry cleaning must be incredibly dodgy and would rather risk shrinking/felting something than have to live with that. (Old hippy). I have done this with incredibly valuable, fine fibres too (am a knitwear designer) and some of the time, yarns labelled dry clean only are oly labelled that because they don't want to risk the potential lawsuits following it being washed badly and therefore shrunk/felted.
If I have made (sewn) garments from pure wool - made a coat from some expensive wool/cashmere from France, last year - I have always pre-washed/shrunk it before even cutting it out, and can't believe commercial tailors wouldn't as well... If the thing is mass produced it may well have been hurridly thrown together and have iron-on interfacing in which case, proceed with caution/dry clean.
But just wanted to say it is entirely possible to wash pure wool items without shrinking or felting, and often that dry clean only label is just because the majority of people will not know how to wash wool (ie: even if being careful, using delicates detergents, might rinse in cold water, wash in warm). For the past 30 years we have made countless things from pure wool (knitted and woven/sewn) and never lost anything we handwashed carefully.
Knitters also know to dry pure wool flat so the weight of water in it won't pull it out of shape. You can also gently prod something back to shape if you dry it flat, on a pile of towels.
I use Ecover delicates or a similar detergent. To sum up:
no sudden changes of temperature - keep wash/rinse baths even temps;
use a detergent for delicates, not washing powder;
no agitation;
dry flat, and supported, so you can 'dress' it back into shape.
If you think it might have iron-on interfacing and be made from not preshrunk wool, dry clean it if in doubt. But my own take on it is, I tend to ignore the label and wash it carefully and if it did shrink or felt or the interfacing puckered - was not worth keeping anyway.
I don't get how manufacturers can't preshrink/full woven cloth to some extent, before cutting out and suspect it might be this cheapness and cutting corners in manufacture that leads them to have to recommend dry clean only?