In The Elder Scrolls there are a few Daedric princes who are relatively new to additions to the group and originally were not Daedric princes at all, like: Meridia, Sheogorath and Malacath.
Are there any more Daedric princes who originally were not Daedric princes?
You mentioned Malacath as a Daedric Prince (a.k.a Daedra Lord), but at least one book says he is not:
He is more commonly know as the Daedroth Prince Malacath, 'whose sphere is the patronage of the spurned and ostracized, the sworn oath, and the bloody curse.' He is not technically a Daedra Lord, nor do the other Daedra recognize him as such, but this is fitting for his sphere.
–The True Nature of Orcs, first appearing in Morrowind
I'm going to define the Daedric Princes as the 16 listed in The Book of the Daedra and Jyggalag, who was identified as such in The Shivering Isles*. This seems to be the most commonly held definition among the people of Tamriel.
Note that there are other definitions. For instance, Mankar Camoran argues that a god can die, but the Daedra cannot, and thus Lorkhan is one of them. However, that's definitely a fringe view.
* I just want to point out that Jyggalag did not make his debut in the second expansion to The Elder Scrolls IV: Oblivion. Instead, his name is in the book On Oblivion, which first appeared way back in The Elder Scrolls II: Daggerfall!
The book On Oblivion refers to the earliest historical record of the Daedra Lords, and describes four by name.
It is most probable that "daimon" is a misspelling or etymological rendition of "Daedra," the old Elven word for those strange, powerful creatures of uncertain motivation who hail from the dimensions of Oblivion. ("Daedra" is actually the plural form; the singular is "Daedroth.") In a later tract by King Hale the Pious of Skyrim, almost a thousand years after the publication of the original Doctrines, the evil machinations of his political enemies are compared to "the wickedness of the demons of Oblivion... their depravity equals that of Sanguine itself, they are cruel as Boethiah, calculating as Molag Bal, and mad as Sheogorath." Hale the Pious thus long-windedly introduced four of the Daedra Lords to written record.
–On Oblivion, first appearing in Daggerfall
Given that the oldest record says that they were what modern people call "daedra", I'm not going to split hairs and say that most were originally "Padomaic beings" because they technically still are (it would be like saying an American was originally a human being).
Most of the Daedric Princes have unknown pasts; they have always been Daedric Princes for as long as people have known them. However, the ones you mentioned are the only ones we know of that were not always Daedric Princes.
Originally the god-hero Trinimac, he got eaten by the Daedric Prince Boethiah and emerged as Malacath.
When Trinimac and his followers attempted to halt the Velothi dissident movement, Boethiah ate him. Trinimac's body and spirit were corrupted, and he emerged as Malacath.
–The True Nature of Orcs, first appearing in Morrowind
Meridia was once a Star-Orphan (also called a Magna Ge), which are divine beings that created the stars in the night sky. One partially translated book says that she had some sort of involvement with the Daedric Princes (referred to here as the "Lords of the Chaos-Realms) and then became one.
This appears to identify the "Daedric Prince" Meridia with the so-called Star-Orphans, those Anuic ur-entities that separated from Magnus when that Divine withdrew from the creation of the Aurbis. The best-known of these Star-Orphans is probably Mnemoli the Blue Star, who is associated with un-time events, and was said to be visible even in the daytime sky at the time of the Dragon Break. [...]
The next passage was quite difficult, but its translation adds an entirely new episode to our accounts of the Dawn Era:
"The Lords of the Chaos-Realms chided Merid-Nunda for her trespass and bade her return to Aurbis, claiming all existing spheres as their own. But Merid-Nunda formed of her substance a great drag-lens, and the light of Magnus was bent thereby. The rays [carved? focused?] a new sphere from the chaos, which Merid-Nunda, [laughing? sparkling?], did claim for her own."
–Exegesis of Merid-Nunda, first appearing in Elder Scrolls Online
As described above, Sheogorath is one of the four Daedric Princes mentioned in the oldest surviving written record of them, and presumably has been in existence for time immemorial. However, the ending to The Elder Scrolls IV: Shivering Isles results in a new person being transformed into Sheogorath.
You now hold the mantle of madness, and Jyggalag is free to roam the voids of Oblivion once more. I will take my leave, and you will remain here, mortal. Mortal...? King? God? It seems uncertain. This Realm is yours. Perhaps you will grow to your station. Fare thee well, Sheogorath, Prince of Madness.
–The former Sheogorath, The Shivering Isles
