Paying in local currency means that you pay whatever the amount is in EGP. You can use any creditcard you wish whether it is issued in UK, US or Timbaktu.

BA in Cairo , I know converts the amount paid in EGP on the day of ticket issue to USD so that effectively locks your Rate of Exchange should the EGP crash the next day!

AA on the other hand, just charges you in EGP as do the hotels. Of course, at the hotels for example, they don't like you paying for the bill in local cash! I wonder if one can try paying for a RTW in local cash?