Problem is not SD Aegi, thats the reason i haven't even mentioned it in the tox scenario, problem is Tox, unlike AV Tan, do not have the raw power to pull it through aegi's subs in 1 hit while in shielded form.
SD Aegi has nothing to do against The Tox because its greatest hit is Head Smash (lool...), and its viable options are shadow claw, shadow sneak and iron head. The tox just haze + scald burns and you already know how this ends. But SpA. Shadow Ball spam is a totally different story. Scald does break standard SpA. Aegi in sword stance, but it receives 30 to 35% in exchange (in a real scenario that should be around 28% after leftys recovery) and, if for some reason it gets a -1 in SpD, Shadow Ball begins to look like this
252+ SpA Aegislash-Blade Shadow Ball vs. -1 252 HP / 252+ SpD Toxapex: 135-160 (44.4 - 52.6%) -- guaranteed 3HKO after Black Sludge recovery
44 to 52% is a range in which you'll be doing recover most of the time, so, it's not impossible by any means to stop it, what I mean is it's not a confortable situation.