The Kaguya KG is a Yang Release. Yang release governs the use of the body and its vitality in jutsu, like the Akimichi's body expansion set of jutsu.
By some coincidence, most healing techniques would also fall under Yang release for the same reason as above.
Consider this also. The Senju as a whole have great physical energy, but only one who was a reincarnation of an uber physical energy guy got to use wood release in the canon series. Tsunade, combining Uzumaki and Senju physical energy uberness, could have her body completely severed in half and still live long enough to save herself and the other Kage, or at least buy time for Oro and company to arrive.
The Kaguya, naturally then, only obtain their KG if they have the incredible physical energy required to perform the Yang release natured techniques. Specifically, the KG allows him to control the bone regulating and creating cells in the body. As the manga more graphically depicts, when he takes stuff out of his body, it generally causes a small amount of bleeding at first. That means that either their healing ability or the differing anatomy account for those injuries.
(middle of the fight between Gaara and Kimmimaro)
http://www.mangapanda.com/93-221-1/naruto/chapter-216.htmlBear in mind, however, that a Kaguya's body is dramatically different than that of the ordinary human. When Kimmi pulled out his spinal cord, it was under the influence of sage transformation (I.E, senjutsu) along with that huge bone forest jutsu that he used. Could he have performed those without the cursed seal? Well, SL headcanon tends to believe so from what I've noticed in the past (recently haven't found a Kaguya, but I recall my fight with Luka).
So, back to the original question. What kind of regenerative power does the Kaguya have? I would imagine their passive regenerative power is considerable, but considering that we never saw anything actually pierce through the Kaguya body, we can assume that it can very swiftly (I would not daresay instantly) close up small wounds in the body. The guy's got such a skeletal structure, I doubt losing a spine (while in that sage transformation state) even affected his ability to stand to any serious degree, nor did it seem to do any noticeable damage.
So I'd say passively without enhancements, it could easily close up small wounds and such without much trouble. Passively, enhanced with sage mode, it could almost instantly patch up small wounds, and very quickly repair more serious ones like the spinal cord replacement trick. That's my view on it.
P.S As a comment towards Shiko areas, pretty much the entire body is a shiko area. The guy could form bone underneath his skin to protect him from getting crushed, so there is really nowhere that could be considered non-Shiko affectable from what I've seen.