Mary Shelley's omission of the decade means she can evoke a general historical landscape from the later 18th c.. But, absent anachronism, the year must be 1799.
Walton refers to Coleridge's "The Rime of the Ancient Mariner," published in 1798. Walton is writing either in that year or, given his travels and distance from England, in 1799, ten years after the fall of the Bastille, six after England declared war on France. Mary Shelley begins the novel in 1816, a year after Wellington defeated Napoleon at Waterloo and so ended a catastrophic series of wars that engulfed the Continent.