I have started bringing my water bottle to work and filling it on my way to the office. There are no public fountains along the shortest route, but there are four I can reach with a little detour. (Four! that's one thing I love about Milan.)
I just checked on a map which detour I should take if I am in a hurry and… the results were quite counterintuitive! The diversion that I thought would take longer is actually the best one, and others that felt shorter are actually worse.