I stir mine with a chopstick every now and again. My sand bed is about 3-3.5 inches deep. It makes the water pretty cloudy but keeps the sand from turning to cement. All of the nassarius snails help keep it in check as well. I've never really had a problem from doing this IME.
I've been stirring it and then skimming real wet for a couple days afterwards. It seems that you would want to stir it and keep the crap out rather than in?
Well I know a little bit about DSB's and I don't believe that your sand bed is deep enough to really help with keeping nitrates down. From that point of view, I would stir it to keep the detrius from becoming a nitrate trap.
If it were me, I'd siphon right through that sand bed when doing water changes. 1.5-2 inches isn't deep enough to be considered a deep sand bed so I'd get out all of the nasties that may get lost in the sand bed before it causes a nutrient issue later