My partner has a similar issue with phones, but she needs one occasionally. She has a cheap clamshell phone and puts $100 on it once a year with T-mobile on one of the pre-pay plans. If you buy the $100 up front then the minutes are good for the full year and you don't have to keep refilling it. I'm not sure about the international details, but they probably offer something related that covers worldwide.

You could also just get a 4G hotspot and use it for your internet habit anywhere, including for skype.