I find it obnoxious when characters who are incognito have some obvious tic. Whether it be fright shivers, nervous sweats, or hemming and hawing every line of every conversation, the only thing more annoying is when only the audience members seem to see it.
Blending in isn't really that hard. If you've ever acted or otherwise performed, you can blend in just fine. Heck, if you've ever told a story that wasn't true (some sort of fiction), then you know how to say things that people would believe, even if they aren't true.
The problem with blending in is that it is usually a black-or-white event. Either the character succeeds or fails. Characters fail more often than not (though not always), because failing is way more dramatic. When you succeed at blending in, there is tension, but no real climax, and thus no significant release of tension. Blending in too well is boring storytelling (though a great example of how "when you do things right, people won't be sure you did anything at all.")
I believe that there are only two ways to really do a blending-in scene interestingly. The first is to fail due to legitimate tells. If a character is in a high security area, where she really is being scanned for authenticity, real-life tics, like averting eye contact or playing with her hands, things that people actually do and usually are unaware of, then it feels like they were genuinely caught and for good reason. The other option is to find the gray between the black and white. If the protagonist is trying to sneak from point A to point B in the guise of a security guard, then maybe the disguise works, but there is a commotion and they are forced off their path due to having to maintain the disguise.
I was very careful with my wording when I said that those are the options to do such a scene interestingly. You can do a classic success or a classic failure scene well - it just has a certain predictability as part of it. If you can do the scene so brilliantly that people don't care that they saw it coming, then by all means go ahead with it.