You can access files in your iCloud account from any internet device, so it would be possible to store the card data or images as text or perhaps jpeg files and access them that way. However that would not be particularly secure unless the data were encrypted and then you are back to having to have specific applications installed on any machine you want to access the data from. Both 1Password and Evernote would work but, you might have to install the app and purchase a license to use it on a foreign machine.
Given most airlines now accept boarding passes on smart phones, is strong reason for traveling with your iPhone along with secure access to Apple Pay, PayPal, and your credit card data or images.
