No, a middle name is improbable at this time.
The Stradlings were Marcher lords, so this line shows up in Peter Bartrum’s Welsh Genealogies, where Edward Stradling is shown married to Elizabeth Arundell.
Burke’s Peerage also gives the name Elizabeth: https://books.google.com/books?id=lF1tAAAAMAAJ&pg=PA509&dq=...
Notes and Queries is a useful and interesting source, but as it’s name implies, it was meant to be a place where scholars sort of worked things out.
I think in this case we can ignore the name Catherine. Skinner has miswritten.
