My new mini-PC came with Windows 10 installed in MBR mode on the internal SSD (/dev/sda). I've got an external GPT-formatted drive (/dev/sdb), on which I've installed Fedora 27 and Fedora 27 (one known working configuration, one to play with; I do tend to fix it until it breaks). The problem: grub on the external drive does not see the internal SSD with Windows 10, so, on those occasions when I do want to boot into Windows, I need to get into the BIOS and switch the boot device. I really don't want to have to do this - what I want is an entry in the external drive's /boot/grub2/efi/EFI/fedora/grub.cfg that will let me boot Win10.

Can this be done without reformatting the SSD to GPT and reinstalling Win10, and, if so, how?

grub2-install --modules=part_msdos

Nope.
Well, not that I've found, and I've had a Win10 MBR - Linux UEFI/gpt for a couple of years. Mine was originally a OEM Win7 Pro, and would not install to gpt. Got upgraded to Win10.
I use Win10 so rarely (racing sims) that it doesn't bother me too much to have to select the boot device - there is usually a Fkey that pulls up the boot list rather than having to go into the firmware, watch your power-on splash screen.