XPS 13 9343, docking station, WD15?

The WD15 is not compatible with the XPS 13 9343 because the WD15 requires USB-C, which the 9343 doesn't have; that arrived with the XPS 13 9350.  There are no official adapters to plug a USB-C peripheral into a USB-A port -- some manufacturers provide them, but the reason they're not certified by the USB-IF is because you can't guarantee full functionality that way.  In the WD15's case, doing that would drop the USB connection down to USB 3.1 Gen 1 rather than its native Gen 2, and you'd also lose display capabilities since the WD15 relies on USB-C's DisplayPort Alt Mode capability, which isn't available from regular USB-A ports.  The only official adapters allow plugging a USB-A peripheral into a USB-C port on the host, but that obviously isn't useful in this case.

The D3100 or newer D6000 would both work, but they both use DisplayLink technology to handle video. That's why it's able to provide video even over a regular USB-A port, but DisplayLink isn't ideal for a lot of reasons.  It would probably be fine if you'll just be using external displays for business productivity content, but things like full screen video and especially gaming will likely be a subpar to unacceptable experience.  That said, that's the only option you have if you want a docking station with that system's available ports.  However, in your position I personally would get a USB hub and connect my display(s) through the Mini-DisplayPort output separately.  That output can drive multiple independent displays if you use either DisplayPort daisy-chaining (if your displays support it) or a DisplayPort MST hub.  You'll end up with multiple cables, but a superior solution from a technical standpoint.