Is it appropriate to use the term "guru" to refer to an expert in matters of Judaism or Jewish law on the assumption that it will be understood as the second definition here, or is it inappropriate no matter what because of the vestigial influence of the first (Hindu) definition?
To judge by Wikipedia, it looks like the basic meaning of it is "teacher" or something similar - the Hindu use of it is a specification of that general meaning. So I can't imagine that it would be any different, say, than our using "priest" as a translation of kohen.
I don't think it's a problem. By this point the word has been integrated into the English vernacular as a synonym for "expert," and does not have any religious connotations.
For example, a quick search of the New York Times results in phrases such as "golf guru," "management guru," "photography guru," "fitness guru," and "fashion guru." In fact, when the Times refers to the original definition of "guru," they explicitly write "Indian guru," and even then it's usually referring to a yoga guru. (Which leads into this question.)
American Heritage Dictionary
Hinduism & Tibetan Buddhism: A personal spiritual teacher.
A teacher and guide in spiritual and philosophical matters: A trusted counselor and adviser; a mentor.
- A recognized leader in a field: the guru of high finance.