This makes me wonder if the update could instead run from a FreeDOS boot flashdisk, considering the note about the "universal format" of the .exe file. But sadly enough, FreeDOS doesn't work with UEFI. I'm not really sure whether switching the machine to the legacy BIOS emulation mode that could hopefully boot FreeDOS would actually make it possible to update the firmware...
FTR, yes, this works, however scary it may seem. :-) You switch the machine to legacy boot mode, boot from a FreeDOS flashdisk (with the BIOS update binary stored on it), run the BIOS update binary and finally switch back to UEFI+SecureBoot upon reboot.
Anyway, having the Dell toolset working directly on Fedora would be definitely less of a hassle. :-)