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Courtesy of the Timatic search tool on Emirates, you are able to Transit Without Visa at both Sharjah and Cairo.
At Sharjah International Airport, remain airside:
If you are transferring from one flight to another, please check for your connecting flight at the βTransfer Deskβ.Transfer and transit passengers SHOULD NOT go through the Arrival Immigration checkpoint.
Again, for your connection in Cairo, you're able to Transit Without Visa (TWOV):
Holders of onward tickets for a max. transit time of 48 hours. This does not apply if transiting through Borg Elarab Airport (HBE).
Holders of onward tickets for a max. transit time of 6 hours if transiting through Borg Elarab Airport (HBE). Leaving the airport is permitted for passengers with transit time longer than 6 hours. Passengers with transit time of less than 6 hours may leave the transit area but not the airport.
IATA Timatic is used by airlines and travel agents to verify passenger travel document requirements for their destination and any transit points. Airlines use various Timatic solutions to ensure their customers are compliant with border control rules and regulations.