Shyness with strangers is definitely neither a necessary nor sufficient condition for being an INFj/EII, though the specific way you talk about it sounds rather Se polr, possibly specifically EII. You talk about it like you're thrown off balance when a stranger initiates with you, so you need to recollect yourself before you can think clearly again. I do relate to this. When a stranger unexpectedly initiates a convo with me, I respond based on what is the safest/most casual possible response, but later I might realize they were trying to flirt with me and if they were handsome, I'd kick myself for not responding optimally.

I don't relate to overall stranger shyness though. I've initiated loads of convos w strangers, and I'm also OK with strangers initiating w me, as long as it's not unexpected (e.g., at a party is fine, but I'll get confused if it's at a grocery store).

Not sure how other types experience shyness, would be interesting to hear. Lots of types can be shy, even some extraverted people can be shy, but I'd guess the shyness happens in different ways and for different reasons.