Short answer: Since Tsunade has never used Poison Mist, or even hinted at being able to use it, it should not be used in conversations about Tsunade in combat.
Your overall theory is flawed. First of all, when did it ever say that Tsunade raised Shizune from birth? Shizune is the niece of Dan, and some time after his death, Tsunade took on Shizune as her apprentice. They do have a close bond, but it is no different from Naruto's bond with Jiraiya or Sasuke's bond with Orochimaru.
With that in mind, using your logic, it is safe to assume that Orochimaru can use Chidori (and all of the different variations that Sasuke has developed). For that matter, Jiraiya can use all of Naruto's techniques to the same degree that Naruto can. If anything, Sakura seems to be the exception to the shinobi rule of surpassing one's master. Nearly every other character in the series has developed their own unique styles and abilities, but Sakura is just a cheap Tsunade knock-off.
Furthermore, why does it even matter? Shizune's Poison Mist wasn't effective against Kabuto. Unless you're thinking that Tsunade's Poison Mist must be on the same level as Hanzo's since Tsunade is clearly a Poison Mist master. Seriously, though. Tsunade has so many other effective techniques in her arsenal, does she really need another weak, B-Rank technique?
