This may appear a surprising choice of diction on Walton's part. Johnson's Dictionary defines the word pejoratively:
Disdainful; squeamish; delicate to a vice; insolently nice.
The Oxford English Dictionary somewhat refines the range of possible meanings:
1. That creates disgust; disagreeable, distasteful, unpleasant, wearisome. Obs.
-- a. That feels or is full of disgust; disgusted.
-- b. Full of pride; disdainful; scornful. Obs.
-- c. transf. Of things: 'Proud', magnificent.
3. Easily disgusted, squeamish, over-nice; difficult to please with regard to matters of taste or propriety.
The connotation of Walton's usage indicates that he is using the word in the third sense here, suggestive of a well-educated and highly refined sense of taste.
What may be most interesting about this sentence is what it says about Mary Shelley's values. A woman who has been "tutored and refined by books" is still an uncommon being in eighteenth-century culture, often referred to contemptuously as a "learned lady." Here, in contrast, Margaret Saville is a paragon of judgment and the conduit through which this entire history, with its multiple internal narratives, flows.