Secure USB cable for charging in untrusted environments

Could I mitigate that risk by taking a regular usb cable and cutting the data (but not the power) cables? Or does the usb protocol needs a data handshake to begin charging?

Such a cable does exist, so a data handshake must not be required.

Such cords are discussed on some Stack Exchange sites:

• Micro USB cables that only charge but no data, no mounting etc (Samsung Galaxy S)
• How can I tell charge only usb cables from usb data cables

So yes, using such a cable or making one using a DIY approach could mitigate a risk that depends on the 2 data pins. Of course, a different kind of attack where unexpected power is sent, possibly with the intent to damage the device, would still be possible.

USB devices can negotiate the provided current from the host device. If power negotiation is not possible (because you cut the data wires), a maximum of 100 mA is supplied. This means you can charge devices, but it may be slower than usual.

Devices such as LockedUSB do the power negotiation on both sides, while not allowing data to pass between devices. This charges your devices faster, but arguably may be less secure than cut wires.

Although not entirely in line with the OP's question, I wanted to share a different solution.

You could take a powerbank with you. Small powerbanks capable of charging your phone at least 1 time don't take up too much space. You can charge the powerbank at the airport terminal, in your hotel, or even on the flight (as there's no risk for malicious data affecting the powerbank). When you need to charge your phone, you can use your freshly recharged powerbank to fill it up.

Another advantage of this solution is that you have a powerbank with you on your trip, should you ever need to recharge your phone in an area where no power outlet is available, or when you don't have your charging cable with you. You can even use the powerbank in other areas where you don't trust a USB outlet.