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The nose can be from a disease process like hypothyroidism. There are creams that are prescription that you can use, you would need to see your vet. For something safe for now...at Walmart in the pet section is a green tin called BAG BALM....ointment originally used for dairy cow teats...can be applied several times to the nose...and see if there is improvement.
No, you were not wrong to be cautious...15yrs is close to the life span of a cocker.
If the skin where the tumors are is still pink, then an occasional wipe with hydrogen peroxide is fine..you do want to prevent infections in a dog of 15!