This answer is based on 3rd edition material, and I don't know whether there's anything in later editions that contradicts this.
The 3rd Ed book "Fiendish Codex 1: Hordes of the Abyss" has some material about what happens to demons slain on the Material Plane. The tl;dr is:
- Usually, the body returns to the Abyss.
- In rare cases it doesn't, because chaos is weird that way.
- Magic can also prevent the body from returning, although the specific spell mentioned doesn't exist in 5th Ed.
- Demonic deaths tend to be spectacular and messy, mostly but not always resulting in swift destruction of the corpse.
Quoting from pages 7-9 of HotA:
...demons are notoriously difficult to study when alive, and when they die, their bodies either return immediately to the Abyss or decay very quickly. Nevertheless, chaos being chaos, some demonic corpses have inexplicably remained available for study.
Capturing a dretch outside the Abyss is difficult, and keeping the creature's body from returning to its home plane after death is almost unheard of. Even so, one ancient student of the Black Scrolls inexplicably did so and managed to document his findings.
"When the dretch died, its muscles quickly atrophied and became very pliable and easy to cut. Thus, I believe the creature's strength stems not only from biological origins, but also from magic... After death, the bones in the hand became brittle, but before the dretch expired, they were strong as steel."
If a demon is killed on another plane, its body eventually returns to the Abyss - unless trapped through magical means, such as a dimensional anchor spell.
By my understanding, there's no official dimensional anchor in 5th Ed, but you could take this as precedent for the idea that magic can preserve demonic corpses, and perhaps persuade your GM to let you research an appropriate spell or item. Dimensional shackles or a modified version thereof would be a likely option.
The book then gives a "Demonic death throes" table, with a d20's worth of suggestions for what might happen when a demon dies outside the Abyss (excluding those like balor which already have a specified death effect). Some sample options:
Nothing special. The demon expires as if it were a normal Material Plane creature.
Its corpse explodes into tiny 1-inch-high duplicates of itself. The tiny demons immediately begin fighting among themselves until only one remains, which then vanishes in a puff of smoke.
The body discorporates into a foul-smelling mist.
Vermin explode out of the corpse, consuming it and then fleeing in all directions.
A hole opens up in the fabric of the universe, and an unseen force sucks the demon into the hole with a loud "pop".
Most of the twenty examples involve total or near-total destruction/annihilation of the body, and most of these happen within seconds, so you wouldn't have time to mithril-plate anything. But there are about three in the list which look like they might allow for salvaging bones.
So, you will probably need to ask your DM about this, and either kill demons until you find one that dies the right way or research some magic that lets you preserve the body. But perhaps that material will give a starting point for those discussions.