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When you travel, always carry a pack of disinfecting wipes. You can use them to clean not just the dreaded remote control, but also the phone handset and doorknobs. The big risks you face from these surfaces are E. coli and enterococci, bacteria that can be transmitted on public surfaces and lead to unpleasant problems.
And since you have them, go ahead and use the wipes to clean off the armrest and tray table on the airplane too.