I used to dry in my ovens, but my minimum setting is 150F, which is too high and hard to control - even if I turn it on for a while and turn it off and then set the cookies in. At 150F, small areas on cookies can quickly over-expand and crack. The icing can even lift off. Typically running a convection oven (with fan running) runs about 25F hotter than a conventional oven - so beware of that route especially.
All said, I MUCH prefer drying in a dehydrator. It's so much easier to control, very rarely do I worry about overheating the icing, and if I get distracted and the cookies stay in longer than 15-20 minutes, there's never been a problem.
But if your oven is well regulated to run at lower temps (95-105F), then it could be just wonderful. That's the temp at which I run my dehydrator.