In a sense, you're trying to prove a negative (that she did not marry). The only "definitive proof" you're likely to find would be a death record (extremely rare in that time and place) or a gravestone (readable stones from that era are few and far between) or published record of a gravestone or reference in a family member's will or a deed that calls her deceased and names her as Hannah Ford (i.e., not under a married name).
However, the records of the First Church of Scituate, as abstracted in The Mayflower Descendant in 1908, include this entry: "Hannah Ford, [the] daughter of Peleg Ford, being sick and in Danger of Death was Baptized privately, at sd. Ford's house 31.6.1719" (Mayflower Descendant 10:227 (1908). (If you have an AmericanAncestors.org subscription, you can see the abstract here; it may be available at a free site somewhere, and most large genealogical libraries should have a copy.)
That's not "definitive proof" that the illness led to Hannah's death, but it's likely that it did. The graves of the Old Cemetery in Marshfield where her father and other members of the family are buried were documented in the Mayflower Descendant in 1910, but the list includes no Hannah Ford. Peleg Ford made his will and his estate was administered in 1769, but the will is apparently no longer extant, and even if it was, it would be unlikely to shed light on the question; Hannah would have been 52 when her father died, and even if she is not named in the will, it would not preclude her from having married and subsequently died.
Why do you need definitive proof?