You can get Skype "worldwide service" free for as many months as you want - as long as you are just calling other computers and not phones. Skype is free everywhere. ;-) Skype costs you only want to call a regular phone or receive calls (get a real phone number). Between two computers, anywhere in the world, Skype is free.
I'm sure there are still internet cafes in Italy at least in the tourist hotspots but fewer and fewer people need them, as more people bring tablets, phones, and laptops on vacation with them and free WiFi is everywhere. No doubt you can find an internet cafe with a Skype camera on its computer.
I'm not sure what "security" issues you are worried about with a Skype account you have setup only for travel? Sure, it's a little scary these days to use a public computer at an internet cafe for anything like your personal email account and obviously unwise to do things like bank and credit card stuff on a public computer. But for a limited use Skype account, what are you worried about? At worst, someone gets your Skype password. (Hint: use a different password for Skype than you use for whatever email account you have associated with it.) I suppose someone could monitor the Skype calls you make, but you'll be making them in a public place anyway without much privacy.
Consider getting a small tablet, netbook, or a smartphone (with forward-facing camera) to take with you instead. Then you can use Skype anywhere there is free WiFi and not worry about people in an internet cafe spying on you. (Public WiFI has its own security worries, but I'd think they are much less than at an internet cafe on a public computer.)