Interesting question and I don't know how you'd do that - maybe using some statically linked binaries for fdisk and mkfs. However, why would you ever want to do that? If you want to remove data from the disk, then just running a suitable "dd" command would wipe the disk. I can't think of any other use case that wouldn't subsequently involve booting from a live iso which would let you format the disk anyway.
One use case is: what if the computer is at a remote location and you'd want to put a new image on the main disk. If Linux is currently using that disk as its root disk, then I suppose you'd have to somehow unmount it, or use a different instance of Linux that runs entirely in ram (so you can kill the original Linux instance and overwrite it).
I guess you could boot into a live installer ISO and get that to install over the root disk, though I don't know what problems you'd face with trying to unmount the original root partition.
If you're wanting to do something like that fairly regularly, then it'd be easier to just run virtual machines (e.g. QEMU/KVM) to do that kind of thing.
