Over and over again, the author uses "should" where "would" would be right:
I don’t know half of you half as well as I should like; and I like less than half of you half as well as you deserve.
I should like to know where it is, if you go wandering again.
‘I should not make use of it, if I were you. But keep it secret, and keep it safe!
Maybe Mr. Baggins has an honest reason for leaving his name behind; but if so, I should advise him and his friends to be more careful.’
Above are just a few examples out of many, many similar instances where it seems like "would" is the right word rather than "should". Of course I didn't find the best examples because I was searching for them, but believe me: there are even less ambiguous cases in there!
Is this supposed to be how people used to talk? Like "ere" is used instead of "before" in many cases? It frustrates me a lot because "should" and "would" have quite different meanings, at least today.