Some time between 1993 and 1996 there was a British tabloid (Express,
Mail, Sun, Mirror or Star) headline that said something along the lines
of Duchess (Fergie) demonstrating a sex toy to Di.  What was the
tabloid and the date of publication?

It appears this was the on or immediately before October 7th, 1996

The only two references I could find:
http://kamps.org/g/?dxle (google groups)
http://kamps.org/g/?yjxf (google groups)

http://www.lexisnexis.com should possibly be able to give a better
answer, but I don't have my login here.

(when will Google hire me as a researcher? :)