Most surgeons are natural optimists. This is a commonly held stereotype I find to be true. They are being sincere. They may not know much about lymphedema either. Mine didn't anyway.
My surgeon said I wouldn't get lymphedema before the surgery. A couple weeks after my surgery he told me if I didn't have signs of it by then I was in the clear. He was wrong. I did get it. I worked closely with a lymphedema therapist for a while and have it well under control. I wear a sleeve/glove when exercising. The strategy is to exercise your arm, very gradually at first, to train the remaining lymph nodes to pick up the slack. Get yourself to a physical therapist who is knowledgeable about lymphedema as soon as your surgeon allows after surgery.
The fact of the matter is you don't really have a choice: You need to have lymph nodes removed. If you leave the cancerous lymph nodes alone you will have far worse problems than lymphedema. I'm sorry. I, too, greatly feared lymphedema. I found it's manageable. You may have to deal with it, or you may not. Either way, it doesn't change the type of surgery you need.