[X] Perhaps an opposite tact should be used. If you were instead an outsider, a loyal Imperial citizen staying at Helgen on the way before… things went wrong, then perhaps they'd buy it: Do'azda name is on none of the lists, any more than any of the other Khajiit are.
[X] Khajiit were well known as traders, even in Skyrim. Pretend to be a local Khajiit trader who'd traded out all the goods to far and sundry and was returning back towards Whiterun. There's a Khajiit community there, worst case she could hope they'd lie for a fellow Khajiit if anyone checked.
[X] The 'Silly Khajiit' routine. Don't give them anything to work with. Do'azda means no harm and she just blundered here… and if you need to find a moment to run away once you're part of the way through, do so.