Are there any wifi chipsets out there that don't have an internal uC or require Linux?
Well, what you want is self-contradicting.

Either, you get a relatively dumb WiFi interface that lets the operating system network stack handle the actual WiFi transmissions (and then you'll need some operating system that does that), or you'll need a system that integrates a controller that takes care of the WiFi handling. WiFi is a tad more complicated then let's say Ethernet.

Hence: You need complex logic somewhere.

Think about what you're about to do: You'll implement something that connects to a network. Something in that system will need to handle all the low-level timing and data layer stuff that WiFi requires. Something in that will also need to handle all the higher level (Ethernet frames, IP packets, maybe UDP or TCP packets, or even more high level above that, some kind of serial link emulated across that; not even to mention crypto and auth). So either you'll need to teach your STM32F4 how to do all that (which will actually be pretty hard) or you'll need some external controller that does that for you and e.g. gives you a simple serial interface.

Even when buying WiFi cards for PCs, you'll notice that these contain extensive firmware themselves. You just can't get around the fact that you need something timing-wise close to the radio to handle all the low-level stuff.

TL;DR: either your WiFi IC needs to be smart, or you need a smart OS. Most of the time, both. You can't have the cake and eat it.