This idea. I like it.
[X] Plan Just a Dutiful Servant
-[X] After ensuring that your appearance will not appear magical, and having Varys check for any hiding guards, greet the Princess under the veil of a courtier come to collect their master's pet.
-[X] Tell her that the cat's name is Balerion, and that you've come to take him back to his owner.
--[X] Make a joke about how cats often are less owned and more owners themselves.
-[X] If it appears reasonable, there is no one else watching, and you are certain that no magic will be triggered by it, remove the dust and spiderwebs from her clothing with a small
working, seemingly bound to one of your rings.
-[X] 'Accidentally' acquire part of a hair in the process - people don't notice a few strands breaking as long as you don't pull them.
And then she'll tell her mother about the nice man who came to take Balerion back to his owner, and who cleaned up her dress with a wave of his hand!
Paranoia thy name is Cersei.