Do you get mechanical clocks these days?

Yes...you might have to look for them in shops that sell antiques & similar look-alikes.
I have seen a few of them here in India, but not sure if you have such shops in dubai. You could try the chinese goods market or Ikea (not sure though but no harm in trying).

 

We are living in a digital era and a nice mechanical alarm clock is rare to find. But if you've an obsession for those retro looking alarm clocks and still want longevity. Then checkout IKEA Store, they've digital clocks with retro styles so that you don’t miss the vintage looks.