Final answer:
The likely diagnosis is Nasolacrimal duct obstruction, as the symptoms indicate a blockage in the tear drainage system rather than an infection like conjunctivitis.
Step-by-step explanation:
The most likely diagnosis for a 60-year-old man experiencing watery discharge upon exposure to dust and mucopurulent discharge when pressure is applied to the lower punctum is Nasolacrimal duct obstruction. This condition occurs when the nasolacrimal duct, responsible for draining tears from the eyes into the nose, becomes blocked. The symptoms described do not align with keratitis, which involves inflammation of the cornea, nor with uveitis, which affects the middle layer of the eye. While conjunctivitis can cause discharge, the presence of mucopurulent discharge upon pressure suggests a blockage in the tear drainage system rather than inflammation caused by an infection or allergy.