I would go with just the stealth roll, if any, needed for the sneaking - not tack on a second chance at failure by adding another roll.
If you really need to make "maybe you sneezed or coughed and alerted the enemies" a mechanical thing, give the enemies advantage on their perception checks to notice the party, or just outright tell the players "The hall is extremely dusty, and will cause your characters to cough and/or sneeze if they walk down it." and let them either figure out how to stop that happening (i.e. covering their nose and mouth with cloth) or choose to let it happen.
I mean, you're not also going to have them make a roll to make sure they don't trip over their own feet while walking on the flagstone floor, or to make sure they don't blink while an enemy is attacking them, right? So why pick out this particular activity as causing a need for multiple successful rolls to accomplish a single action as intended?