the reasion you do not have a win 10 listed updater is because HP never certified this OS on that model system
in most cases you can run the win updater under win 10, but a safer method is to use the DOS updater which is also included in the bios package
download the current bios, and then use WinZip or WinRar or 7zip, to extract the files/folders in the SPxxxx file
now create a bootable USB key with "RUFUS", and copy all the files from inside the SPxxxx\DOS folder onto the USB key
read the help file that describes how to run the updater under DOS
reboot (if nessary select boot from USB first in your bios or boot options) from the usb key, run the updater