AFAIK Mr Garmin doesn't do such an item BUT the standard handlebar mount that fits with two "elastic bands" could very easily be mounted on a nylon watch strap to do what you have in mind - probably with a bit of sewing around the "horns" that the bands clip into. [I assume you are aware it fits into a mount with a twist and lock mechanism]
... on the club run yesterday I had the Garmin Edge Touring on the bars, with map etc, and an Edge 200 in my jacket pocket - that worked fine to record the whole trip (the Touring was used for just part of the day)
Rob