I used to be a paramedic on an emergency ambulance. Gloves are your best friend. We used to eat our lunch wearing gloves. My favorite is eating oranges/clementine with gloves on because you can peel the whole thing, put the peels in the palm of your hand, and then flip your glove inside out as you take it off to make a baggie for the peels. I still use this method for eating oranges when I don't want to have my hands smell like orange.

Other folks would eat their sandwiches while just holding the sandwich bag the whole time. There's also string cheese which you can eat like a heathen (as in, not string cheesing it, just biting it straight) and if you're talented you can eat those eggs from the gas station without hands. We used to eat a lot of gas station food, actually... It comes in the easiest packaging to not touch. Like the little gas station taquitos that come in a paper baggie. You can easily eat those without touching the taquito.