A very interesting topic, Inziladun.
I'd say the Morgul wounds and Black Breath are the result of spiritual doings, simply by their nature and the fact that they seem very medically "clean." I find the surgical/treatment aspects interesting too, and also suggestive of spiritual wounding. I know the herb athelas is used, but in surgical terms Elrond would have had to practically cut Frodo in half to get that splinter out, and there is no evidence that he has done so when he wakes up in Rivendell, so the suggestion is that he has somehow "charmed" the splinter out. Gandalf says that it has been "melted." But did Elrond extract it with his own spiritual powers, and did it melt upon contact with the air? This seems more likely than it being melted within the body - the poison would have remained in Frodo's body had that been the case. By "medically clean" I mean small, clean wounds, not gory, festering ones, and not cured by surgery of the "cutting" kind.
In a way, you could compare the "drag of the ring" to this. It is a terrible weight to Frodo, which burdens his body as well as tormenting his mind, but it leaves no physical trace. The chain upon which it hangs does not cut into his neck (as it does in the film), but the Ring does exhaust his body as well as his mind. In my opinion, this is a spiritually evil force affecting the body - the Ring trying to save itself by immobilising its bearer - since it allows Frodo's strength to rush back when Gollum attacks him. It also allows Frodo to walk upright the rest of the way to the Sammath Naur. I think either the Ring knows that it has won by then, that Frodo is unable to let it go, or it is simply that Frodo is no longer resisting it, so there is no weight or torment. (Sorry, I have digressed a little here).
My gut feeling regarding the plague that killed Lalaith is that it would have been a mixture of spiritual and biological disease/pestilence. Morgoth's spiritual power harnessing germs or pestilences and augmenting/spreading them. After all, there are germs in Middle-earth already, such as the mild one that caused Bilbo to say "Thag you very buch." (Because I don't think that could can really be laid at Smaug's door (I'm joking, of course - see next paragraph).
Being in cold water all night would give you a nasty cold in the Third Age, just as it would now. Also Frodo, shivering in Mordor, says "It's gone cold, or else I've caught a chill." And of course there must be many more fatal illnesses common to the Third Age and now. Frodo thinks "Perhaps he had been ill?" when he wakes in the Last Homely House, and one would presume a fatal illness carried off Bilbo's parents, Sam's mother, Widow Rumble's husband, etc. Of course, I'm stating the blatantly obvious here, and there is also the reference to the "leechcraft" of Gondor in the Houses of Healing episode, and the herblore of their master - there are remedies for such things as "headaches."
Which brings me to the "dragon sickness" which the Master of Dale fell under, and the unwholesomeness of Mirkwood. In the latter, I think the spiritual uncleanness of Sauron mingled with nature and infected it in a "biological" sense as well as a spiritual one. The "dragon sickness" seems more of an enchantment, though - a spiritual illness. Perhaps spiritual disease mingling with metals (treasure/swords) results in more spiritual woundings/illness, whilst when it mingles with nature (water or plant life) it becomes more biological. So - mingling with animal/human life - it seems to be both. In the case of the Morgul blade, a spiritually diseased knife causes a spiritual illness, and attempts to effect spiritual death/wraithdom. But it also causes severe physical pain and works towards the heart (physical/biological illness). However, the "physical" scarring it leaves appears to be quite invisible. It must be there, because the physical pain recurs when Nazgul are near (and I'm not even sure it needs to be the particular Nazgul that caused the wound, viz the flying one whose steed Legolas shot down when they were rowing down the Anduin) and upon anniversaries.
I am also reminded of the flowers which are "beautiful but horrible of shape" and the "charnel shapes" in Book 4 of LOTR and the horrible diseased land on the borders of Mordor. The latter is near the Black Gate, IIRC. The former, I think, is near Cirith Ungol, but I'd have to double-check to be sure. Lands do seem to become "biologically diseased" when an evil
fea resides nearby. Also, I think Faramir warns Frodo and Sam not to drink from certain rivers. Diseases affect not only humans, but the natural world as well.
The enchanted stream/river in Mirkwood that causes forgetfulness is an interesting case, too. But given that Ulmo is a good and powerful
fea who is connected strongly if not entirely with water, I wonder if lesser spirits on the side of evil might cause such enchantments. Fire spirits lurk in Middle-earth still, for instance. As Gandalf (I think it is he) says, "There are older and fouler things than orcs in the deep places of the world."