Looks like the links are getting all messed up.

The Windows env required update:

Chipset

The BIOS update: 

Thunderbolt 3 update

Has anyone applied the 2nd without applying the first?

I have not had a chance to build a w10 thumb drive that would allow me to apply the updates in the right order, but I did find that for f23 kernel 4.4.6 that if I use nomodeset and i915.modeset=0 for kernel startup options that having the TB15 dock plugged in no longer hangs.

Still working up the courage to apply the BIOS update without first doing the chipset update.

How is it even possible to apply the second one without possessing a Windows to boot from?

You can make a USB stick which has a windows environment and the BIOS update executable:

www.dell.com/.../en

NB Make sure to check the checksum on the bios image.

NB Some laptops may require a switch from UEFI boot to legacy boot for the unetbootin image to be seen.

Tried to boot from the prepared USB stick, as described in the link you posted, but I always run into a cursor that simply just blinks. No boot menu or such where I could chose `fdos` or something similar.

Note that I had to fall back to legacy boot to start from the USB stick. Tried it with two different USB sticks.

I've not been able to.  When I prepare the DOS boot image, it boots OK, but says I need windows to apply the thunderbolt update.  That's not useful.

I think this was answered already, but the chipset one requires a windows 10, the other just any old boot method. i think you can actually just put the BIOS update on the EFI partition then do an F12 to grab it (not tried it).

My only concern was the W10 part. It's listed as a dependency.

I just tried multiple methods to build a W10 thumb drive (my XPS 13 was windows before it was fedora 23) but no luck so far. I used wimapply and manual partitioning. Then used bcdboot from an installation media thumb drive to set the bcd boot file correctly. No joy so far although I thought I did everything correctly.