In the phrase かといって
or かと言って
, meaning having said that, on the other hand
, I'm not sure what the か
and と
are.
My first guess is that these are the generic particles (か+と+いって), but I couldn't find any evidence to suggest that (or, for that matter, to refute it).
Of course, I could be over thinking this, so it could be a "that's just how it is said" kind of phrase.