Both the Pharaohs canal and the Arab canal were not located where the 19th century canal would be dredged. They used branches of the Nile delta, and were sized for galleys or barges. There was the need of periodically dredging the silt, but manpower would be available in the Delta region which was the breadbasket of Egypt. Over the centuries, the branches of the delta changed their paths but it was always feasible to use new branches with relatively minor improvements. IIRC the ancient canal had only one permanent stretch, about 40 km long which connected to the Bitter Lakes: this artificial canal was discovered by archeological teams.
This solution would have certainly be feasible in the 16th century: it was just a matter of identifying a party which would have an economical/military interest in funding it. The Mamelukes were not interested on their own, and the Ottomans were also lacking interest for a number of reasons, chiefly among them the fact that it would compete with the already established trade routes in the Persian gulf as well as the lack of focus in competing against the Portuguese in India (the only serious attempt was in 1509, in alliance with the Mamelukes and the sultan of Gujarat and with some support from Venice too, but the defeat at Diu put an end to any Indian strategy).
The only plausible player could have been Venice, in alliance with the Mamelukes. The strategy was there, but Venice had also much closer focuses to monopolise their attention, and ultimately the ottoman invasion of Egypt closed the window of opportunity.
Economically a mark 3 version of the pharaohs canal might have worked, using oared galleys and barges, and trans-shipment would not have been a serious drawback, since all the trade routes from India to Europe were long and often dangerous. Even from a military/strategic Pov this canal would have worked. Ships like caravels could be towed, and their cargo and guns transported separately. Even more easy would be to ship timber, ropes, sails and guns to an arsenal to be founded at Suez.
It would have been a major undertaking, but also a potentially history changing move.