Definitely do not dry clean your jersey...any dry cleaner you take it to will (or at least should) tell you the same.
The CCMs I play in I machine wash in cold, tumble dry low.
My CCM Brodeur jersey says the same thing...do not iron, bleach, dry clean or stir fry. But I've only hand washed that one and air dried it. That would be the best option, IMO.
Let us know how you make out.
I wash ours inside out, cold water, gentle cycle if I have to do it at home, but I prefer taking my autographed one to the laundromat and using a front loader. That's because I don't trust the stitching with a wringer washer. I've had no problems drying in the dryer on the lowest setting.
There should be two tags...one on the collar and the other will be sewn on the inside of the jersey on the left side.
Authentics do not have a care tag.
Machine wash gentle, warm water is fine, to keep your crest in good shape. Do not use fabric softeners or machine dryers. Hang dry and i siggest folding a towel in half long way and drape over the hanger under the jersey while it dries.
OxyClean will not damage your jersey, should you need to remove any stains. For tough stains you can mix several cups of it into a gallon/gallon and half of water and let soak over night.