Several varieties of bagpipe I'm aware of don't even require breathing, since they're powered by bellows. The pipes are surprisingly hard to learn by the way. One normally starts on the chanter, which is more like a recorder and is not bag assisted.
>One normally starts on the chanter, which is more like a recorder
In the case of the Great Highland bagpipes, the most similar traditional instrument is the rauschpfeife (capped double-reed with conical bore and without prominent bell):