He doesn't swing in the sense Cannonball does, but he was a unique voice, and instantly recognizable. His sound alone marks him as one of the unique players in Jazz, but his sparse melodicism is also unexcelled.
The general feeling always was that Paul Desmond provided the swing behind Dave Brubeck, who was technically interesting, but rhythmically a bit stodgy. Happy to be corrected by Brubeck's supporters. However, what is rarely denied is that Paul was an exceptional artist in his own right. Always inventive. Rarely playing anything dull.