How do I start a Windows 10 partition on a MBR partitioned disk on a system that otherwise uses GPT/UEFI GRUB?

Okay, let me explain. This is a UEFI computer. It has two disks. The primary disk is partitioned with GPT and boots via GRUB2 to an Arch Linux partition. The secondary disk is partitioned with MBR and only boots if I disable the primary disk in the UEFI setup utility. The secondary disk has a partition with Windows 10. My question is how do I add a menu entry to the primary GRUB2 configuration that boots the Windows 10 partition on the secondary disk? I tried

-mkconfig

with

-prober

and it was unable to find the Windows 10 install. There's apparently nothing wrong with the Windows 10 install, since it boots just fine on its own. I then tried manually adding various menu entries to the grub.cfg but they didn't work. Below are some of the entries that I tried.

menuentry "Windows 10 (loader) (on /dev/sda3)" {
	insmod part_msdos
	insmod ntfs
	insmod ntldr

	ntldr (hd0,msdos3)/bootmgr
}

menuentry "windows 10 (loader) (on /dev/sda3) 2" {
	insmod part_msdos
	insmod ntfs
	chainloader (hd0,msdos3)+1
}

menuentry "Windows 10 (loader) (on /dev/sda3) 3" {
	insmod part_msdos
	insmod ntfs
	chainloader (hd0,msdos3)/Windows/Boot/EFI/bootmgfw.efi
}

The most successful one is the last one which apparently boots to the EFI FW program but gives a BCD error (which is not present when booting normally.)