Is there any lymphadenopathy (swelling in the lymph nodes)? You or your doc can check the ones in the neck. That would give you a good clue as to the kinds of systemic involvement the lesion has. Swollen lymph nodes could mean cutaneous lymphoma. I lost my six year old dog to a particularly aggressive, incredibly rare variety last winter (panniculitis-like cutaneous T-cell lymphoma). He, however, had literally dozens of skin lesions that cropped up almost overnight as well as severe lymphadenopathy. There are other kinds of cutaneous lymphoma that have much better prognoses.
Fortunately, there are all kinds of cutaneous lesions that don't mean lymphoma or even malignant cancer at all. You may find out that the lesion is a completely isolated problem. If the vet fears cancer, the lesion should be biopsied immediately. It it can safely be removed entirely in the process, so much the better.
If the lymph nodes are swollen, they can be aspirated with a needle, and the aspirate can be sent out for testing. Needle aspiration is a procedure where they stick a needle into the node and grab a tiny piece for testing. It's an uncomfortable procedure for the dog, but not horrible, and there's no recovery time once it's over. Needle aspirates aren't always conclusive, so your oncologist may recommend (again, only if the nodes are enlarged), a full biopsy of a piece of the node, which does involve an incision, stitches, and some recovery time.
Another possibility is mast cell tumors, which have a better prognosis, particularly if the one on the muzzle is the only one. I think I recall that mast cell tumors are much more common than cutaneous lymphoma. Again, a biopsy of the lesion would be necessary for diagnosis, and removal of the lesion would be ideal if possible.
Dogs also commonly get benign fatty masses called lipomas as they get older, and those can just be removed. The masses can break open and cause sores. That would pretty much be the best news possible about this lesion, though if your vet said "cancer," that means he or she probably ruled out a lipoma first.
Keep us posted. Many of us have dealt with all kinds of the common cancers and chosen different treatment options, so we can provide support at the very least. Here's hoping that the sore is just a sore.