GRUB 2 scripting: convert device name in GRUB notation into a Linux device name

I'm trying to use partition labels (or UUIDs, that does not matter) to select root partition without use of an initrd/initramfs.

With initramfs, this is fairly easy: root=LABEL=... or root=/dev/disk/by-label/... in the kernel arguments does the job. However, without initramfs the above is not possible: the LABEL= notation is decoded by initramfs script, and /dev/disk/by-label/... symlinks are created by udev running from the initramfs. Only the root=/dev/sdXY notation is understood by the kernel itself.

However, GRUB supports shell-like scripting, and I think that it is somehow possible to write a GRUB 2 scriptlet that will generate root=/dev/sdXY string from a device label or UUID.

Especially, the command search --label <label> --set ROOTDEV will set variable ROOTDEV with a string like hd0,gpt5 which points to the partition with given label. If I understand correctly (please correct me if I'm wrong) the order of devices in GRUB and kernel is the same, so hd0 is /dev/sda, hd1 is /dev/sdb and so on.

So here is a question: is there a way, from inside the GRUB 2 script, to convert hd0,gpt5 into /dev/sda5? Exactly the hd0 into sda part - the rest is easy with regexes.