Finding good accommodation in the beach destinations at the last minute will be tricky, or at the very least, much more expensive than it would be booking ahead. The largest groups of tourists in Croatia - Germans, Slovenians, Italians, etc. mostly book weeks if not months in advance. Minimum stay requirements are very common in those destinations, even as much as 7 nights isn't unheard of - Saturday is often considered to be the "change day", it's also when traffic is the absolute worst in this part of Europe. I'm not implying you'll be required to stay for 7 nights, not at all, it just means that your accommodation options will be automatically more limited. Granted I have no experience using Airbnb in Croatia, we usually either go to a hotel or private self-catering accommodation booking the old-fashioned way, so your experience may differ. Otherwise, those ladies with the "sobe" signs are always a last resort, as Agnes mentioned, although they are a bit of a hit-and-miss affair in my experience.
That said, I generally find booking isn't really necessary when in the interior of Croatia, most tourists stick to the coast, so if you'll be travelling inland it shouldn't be such a problem. On the coast, especially on the smaller islands, on the other hand, do try to book ahead if you can.
And regarding the crowds, apart from some places like Dubrovnik when the cruise ship passengers arrive, you will rarely find places to be shoulder to shoulder crowded.