Where in Europe are you flying from? Your options to Cairo are to go via:
- London with BA
- Madrid with IB
- Amman with RJ
- Casablanca with AT
Depending on where you're coming from, I would look at connecting through London or Amman as they generally have the shortest total travel time. Iberia has quite a few European destinations as well, but they only fly once daily (as opposed to 2x from London and 4x from Amman).
AY doesn't fly direct from HEL, so you're out of luck there. You
could do something like HEL-LHR-CAI if you can only find a flight into HEL.