Which is more unlikely, choosing a Speaker from outside the House membership, or shutting down Congress because they can’t find anyone within it able to garner 218 votes? If we’re not at the latter now we’re at least closer than we’ve been in a long time. The Conservative minority might even take the shutdown over another RINO speaker.
Why would that shut down the House? The Constitution says that the House shall choose its leaders; it doesn't say that it can't meet without a Speaker. If Boehner were to walk away tomorrow that doesn't mean the House disbands and goes into hiatus until a Speaker is chosen.
So to answer your question, there is zero chance that the House will choose a Speaker from outside of Congress. And there is the same chance that the House will shut down due to lack of Speaker. So both are equally unlikely.