Absolutely, I imagine the insurance alone would make the Persian Gulf route unviable. Pirates is one thing, but governments confiscating boats would be a huge disincentive. The other side of the Sinai is probably much more palatable even if Egypt and Israel aren't best buddies.
Not to mention the terrorism/sabotage/non-state actor destruction opportunities that route would present that are moderately prevented on the Red Sea side (if you can get past the Horn of Africa).
I can't see Egypt approving an alternate canal that Israel would have any control over, but I could absolutely see Israel going in on a chance to a) take business from Egypt and b) add a defensive feature along that border.
Both a) and b) would require a real increase in tensions. Israel and Egypt have a cold peace, with several common enemies/interests; the prospect of a direct military confrontation is nil, and neither side will go out of their way to harm the other economically.
