Invasion of Egypt
Actually in Apr '41 & Jan '42 there were detailed plans to invade Malta, which in '42 would have involved the German 7th Flieger & 5th Gebirgs Divs (from Crete), the Italian Folgore parachute & La Spezia airlanding divs (from Sicily), & 70,000 additional troops. This would have ended the disruption to Rommel's supply lines, it would have enabled the Germans to put a 3d panzer div & a 2d motorized div in N Africa, & it would have gotten him to the Suez before the Torch invasion. This made it a better option than your direct invasion of Egypt. Both of the Malta invasions were derailed by Rommel's disobedience of orders, pressing offensives when he was told to stand fast.
The beauty of the Malta plan was that it was an island, relatively isolated from immediate Brit reinforcement. Your invasion of Egypt, on the other hand, would put German (& possibly Italian) airborne forces in the middle of a Brit theatre of war, caught between Brit forces in the Middle East & those in N Africa. Yes, existing transport planes could range Egypt from bases in Crete, but that's only part of the equation. It's too far for them to deliver resupply within a single day (unlike Malta), so Axis forces would be on the ground for 24 hours or longer with just the ammo they'd jumped with. Also, the Brit fleet at Alexandria would interdict naval transport, so you'd have no ground reinforcements, no naval gunfire support, & no naval resupply. The Axis had just 4 divs, identified above, that were capable of such an op-- all infantry-- & they'd be facing strong Brit armoured units. In short, they'd last about a week. Maybe not that long.
Of course, expending all 4 Axis airborne units might be acceptable in a "Market Garden"-type operation where DAK would press an offensive at the same time, intending to link up with the airborne guys. The only time this would have been feasible was during the El Alamein op, but during 1st Alamein it wouldn't have been possible to plan because no one knew when Rommel would reach El Alamein, & after that it would have been impossible to execute because of the immense strength of the Brit 8th Army, & also because Rommel was out of gas, & almost out of panzers.