Divide and conquer
Don't keep everything together. Keep the account data you copied in a separate location from your actual cards; there's no sense keeping it in your wallet or handbag, because you'll need that info if you get pickpocketed or fall victim to purse snatching.
You may wish to bring only your "main" card and leave your backup card in the in-room safe. John Sileo, a professional speaker and consultant on the topic of identity theft, advises against leaving valuables in a central safe by the hotel's front desk. A large number of staffers probably have access to that, he says, which could make your information susceptible to theft.
If you brought digital copies of your information, make sure the folder or drive in which they're stored is encrypted, so even if someone gets the actual device, they can't access your data.