I took a look at the Dell page, since it is *.EXE, you are limited to a DOS or Windows install.
On the Freedos website
http://www.freedos.org/download/ you have a legacy CDROM FreeDOS 1.2 install.
You will need to have a modified version of the iso that includes your BIOS *.EXE file on the CD itself.
Download the iso, then mount it.
su
password
md /mnt/d
mount your_freedos_iso /mnt/d
ls -l /mnt/d
you should see the file system at this point, and be able to copy the exe into the root directory.
you will probably want to edit the autoexec.bat in the root directory and add "pause" somewhere before the installer, or insert "rem " or "remark " in front of the installer steps, but I think you might be able to <CTRL-C> the install process, so it's probably unnecessary. then:
umount /mnt/d
and create your freedos CDRom.
during the CDRom boot process, you should be able to <CTRL-C> break the process and see a DOS prompt. At this point, you can run the dell BIOS program.
Some EXEs will refuse to run from freedos - if this is the case, you'll probably need to make an msdos cdrom, google found this
http://www.optimizingpc.com/install/bootcd.htmlCDroms are read a little different from USB, and are a bit older tech.
The fact that you are able to boot a USB containing Mageia is a good sign, it means you can boot a USB stick. Mageia takes care of itself by loading appropriate drivers, but DOS, you would need to find drivers to get you past the black cursor problem. This may be a challenge.
I think Dell supplies install or recovery CDs - you may have to resort to installing/recovering a windows OS simply to run the BIOS update, but as you're installing Mageia 7, I'll guess you might not mind if you're doing a fresh install anyways.