They really wouldn't have that many other options especially since using Israel as a pretext was pretty
underpants gnomes to begin with. The reason they tried to use Israel as a fig leaf was because they knew neither the US or the USSR would accept such blatant gunboat diplomacy as any even more transparent intervention would've been. Granted using Israel, who was widely known to not seek aggressive war at the time without an outside ally's support and blessing, was pretty stupid to begin with but that really shows where they were at. It's worth keeping in mind to the British the Suez Canal was the jugular vein of their crumbling empire and for the French they widely suspected (with good reason to) that Nasser was helping support the Algerian independence struggle and they were fighting to hang on to the only colony they considered to be an extension of mainland France. For two declining imperial powers doing nothing to stop the nationalization of the Suez Canal was unthinkable but they also knew actually doing it for those reasons would not be tolerated by the new superpowers.
Maybe they go for something more transparent (and stupid) with enough time and pressure but that's likely to end even worse than what they did in the first place.