I got onto a plane in Dallas with only my phone, as I lost my wallet.
How? In this day and age of we must harass you or the Terrorists will win?
I have pictures of my ID, my health insurance card, and my passport, on my phone. I also have my debit cards too...I do this in case I lose my wallet, obviously. I have all the info I need to identify myself, and can cancel my debit cards easy. The airport security was quite happy to take the pics of my "IDs" as ID to get on the plane.
Now, if the phone thing scares you, email jpeg of all this to yourself. Then, you can access them at will, from almost any device...
Sometimes, insurance is you protecting yourself...from yourself.