Nearly impossible. The 1.6 is the 128 block and the 1.4 (I'm guessing you mean the 1368cc 16V) is a SuperFIRE engine. The mounts are all different, gearbox and linkages aren't compatible. The 1368 will not bolt up to your box. If you had a 1.2 16V convertible the 1.4 is pretty much a straight swap.
To make that engine fit your Punto you would need the mounts from a 1.2 16V and a complete donor (like the Idea I have in the classifieds).
The 1.6 Bravo/Brava/Multipla 16V is a bold in conversion but you'll need a complete donor for the loom and bits. Personally I would use the donor airbox and bits as well so it looked completely standard.
Unless you're on about the older Tipo/Uno/Fiorino 1.4 8V then it's a straight swap but the weight of the cabriolet could be a bit much.