This is probably Edward Lucas White's "Lukundoo".
"How is he treating the swellings?" Van Rieten enquired.
"He slices them off clean down to flesh level, with his razor."
"What?" Van Rieten shouted.
Etcham made no answer but looked him steadily in the eyes.
"I beg pardon," Van Rieten hastened to say. "You startled me. They can't be carbuncles. He'd have been dead long ago."
Van Rieten passed one of the heads to me. The sun was just setting and I examined it closely. A dried head it was, perfectly preserved, and the flesh as hard as Argentine jerked beef. A bit of a vertebra stuck out where the muscles of the vanished neck had shriveled into folds. The puny chin was sharp on a projecting jaw, the minute teeth white and even between the retracted lips, the tiny nose was flat, the little forehead retreating, there were inconsiderable clumps of stunted wool on the Lilliputian cranium. There was nothing babyish, childish or youthful about the head; rather it was mature to senility.
"Where did these come from?" Van Rieten enquired.
"I do not know," Etcham replied precisely. "I found them among Stone's effects while rummaging for medicines or drugs or anything that could help me to help him. I do not know where he got them. But I'll swear he did not have them when we entered this district."
Stone was clean and not emaciated, but he was far gone; not unconscious, but in a daze; past commanding or resisting anyone. He did not seem to see us enter or to know we were there. I should have recognized him anywhere. His boyish dash and grace had vanished utterly, of course. But his head was even more leonine; his hair was still abundant, yellow and wavy; the close, crisped blond beard he had grown during his illness did not alter him. He was big and big-cheated yet. His eyes were dull and he mumbled and babbled mere meaningless syllables, not words.
Etcham helped Van Rieten to uncover him and look him over. He was in good muscle for a man so long bedridden. There were no scars on him except about his knees, shoulders and chest. On each knee and above it he had a full score of roundish cicatrices, and a dozen or more on each shoulder, all in front. Two or three were open wounds and four or five barely healed. He had no fresh swellings, except two, one on each side, on his pectoral muscles, the one on the left being higher up and farther out than the other. They did not look like boils or carbuncles, but as if something blunt and hard were being pushed up through the fairly healthy flesh and skin, not much inflamed.
The swelling on his right breast had broken. Van Rieten aimed the center line of the light at it and we saw it plainly. From his flesh, grown out of it, there protruded a head, such a head as the dried specimens Etcham had shown us, as if it were a miniature of the head of a Balunda fetish-man. It was black, shining black as the blackest African skin; it rolled the whites of its wicked, wee eyes and showed its microscopic teeth between lips repulsively negroid in their red fullness, even in so diminutive a face. It had crisp, fuzzy wool on its minikin skull, it turned malignantly from side to side and chittered incessantly in that inconceivable falsetto. Stone babbled brokenly against its patter.
What doesn't match is the actual presentation of the story. "Lukundoo" is largely the account of two explorers as they try to determine what happened to Stone. Stone barely speaks before dying, and he states that he was not cursed, but that his affliction came from within.
Found by searching for "short story" "witch doctor" curse heads, which brought up this LibraryThing dicussion.