Actually, I have heard of the instrument. This is a result of having a degree in music and growing up with a mother who taught and performed on recorder and did various old music performances (I once performed some Henry VIII music on crumhorn for my high school history class). That said, I don't recall ever having seen an oboe da caccia or hearing one, beyond those on recordings.
BTW, the organs used as part of the continuos (often played with a keyboard instrument and viol or bassoon for the bass line) are those small brown keyboard instruments on the stage, at least one them. They are often referred to as "postiv" organs and only contain a couple sets of pipes with a single manual (i.e. keyboard). I would not have been surprised if they had manually pumped bellows on those, but I do not see any lever though the sitting organist could be pumping by pedal.
Thanks for the post, Volkonski.