As long as you get some 16" alloys from an SE model for example, you shouldn't have any problems.
I wonder about TPMS sensors, your EX might have them, but SE alloys may not.
It's all possible, but with some expense.
Even on 16" our Jazz S doesn't have the smoothest ride, I have to say, so your gains will be marginal.
We've just got a Seat Ibiza in the family on 17" wheels, and I'd say that's a smoother ride than the Jazz.