Hi I opened your blend file and see a lot of node structure for the materials, i am not very experienced with nodes/materials on blender itself, but just by clicking on each object it seems the part that you cant get rendering right seems to be slightly different in the node structure?
But anyway, asides that, I downloaded your blend, looked in blender and without changing anything i directly uploaded your model to sketchfab, and I don’t see that part rendering black at all? I did however see that part render a pure white color, so what I did was selected the other parts and copied the hex value and applied it to the hex in the diffuse of the part that was not the same color.
and this seems to match the other parts.
From what I see from your shaded view in blender I see you have some other things going such as a bit of bump texture and so on, so I simply tried to recreate something roughly similar in sketch-fab itself using this simple texture
Used for the fine bump texture / edited the UV scale on sketchfab to adjust that and the 2nd instance I used with cavity , combined I think gives a decent bone texture effect.
Along with that I used subsurface scattering (no texture images used)
and in the post processing settings I used ambient occlusion, a tiny bit of depth of field, a hint of bloom, some tone mapping tweaks and very subtle color balance tweaks
No dynamic lights just the default hdri environment lighting along with sketchfab ground plane with baked ao shadowing
this all took about 5 mins
(note, this is a private upload and I will delete it after you have taken a look)
So, I am not sure why you are seeing black when uploading to sketchfab and are unable to change the map on that particular mesh part