The k'suva text varies slightly depending on whether the bride is a virgin, independent of whether she has been married previously. (For one thing, the amount of money mentioned in it is different; for another, the word "בתולתא" is omitted from the k'suva of a non-virgin.) Now, there's a custom to read the k'suva aloud during the wedding ceremony. I have heard that, in the case of a non-virgin bride whose non-virginity may be a source of shame (e.g., she has never been married), the person reading the k'suva aloud reads it wrong deliberately, reciting instead the text of a virgin's k'suva, so that no one else hears that the bride is a non-virgin. I am looking for a source that indicates that that custom (of deliberately misreading the k'suva) is appropriate, inappropriate, practiced, or not practiced, or any source or provenance for it.
For starters: in Ashkenazic custom (which I think the questioner was assuming), the kesubah has already been signed (i.e. executed) before the chupah, so the reading is nothing more than a pause between parts of the ceremony. It's accomplishing nothing of a halachic nature any more than reading the latest stock numbers would be, hence many rabbis have been lenient in exactly what's read.
This gets a bit trickier in the Sephardic world as the witnesses are signing it on the spot, under the chupah. They're announcing it as it's executed. It could seem weird to proclaim you're executing a document with terms A when you're secretly executing a document with terms B. I don't know what Sephardic rabbis would say about this.
Just to clarify: if a woman was born Jewish and never previously married, and was never involved with a non-Jewish man, then the appropriate word to both read and write is in fact besulta.
Igros Moshe OC4:118 -- addressing a religiously-serious young woman trying to repent for what she did in college:
The questions come up when it's not widely known that the bride was divorced, widowed (very unlikely), converted, or had a non-Jewish boyfriend at some point. (In the latter case ideally it'sa is written if that's actually known, though don't ask me how often rabbis actually ask about this.)
Rabbi JD Bleich has a yutorah mp3 in which he says if the bride is visibly pregnant, you can still in theory write besulta, but if so the rabbi shouldn't sign as a witness on the kesubah. While technically valid, it makes the rabbi's personal credibility look shaky.
As to your question, I suspect a lot of this remains oral tradition, not written down, for obvious reasons; I was told of an instance where Rabbi Yaakov Kaminetsky had someone write a dummy kesubah for the purposes of reading, and I spoke with a seasoned moreh hora'ah who had a similar instance where he said "who says that what's written there is what you have to read?"
Afraid I don't have written sources.
This is an excellent question that is best asked to your local Orthodox rabbi.
One important aspect of the question, which should not be minimized, is the public humiliation to the bride, who will be mortified that her lack of virginity will be revealed to her friends and family. Chazal say (Berachot 43b) about embarrassing someone in public that it better to cast oneself into a fiery furnace, that one who embarrasses someone in public has no share in the world to come (Avos 3:11) and that it is comparable to shedding of blood (Bava Metzia 58b). On a day that everyone has an obligation to cause the bride and groom to rejoice, to cause a measure of public humiliation would seem non-ideal, to say the least.
Another important aspect of the question is the halachic importance of reading the Ketuba under the chuppa. Rav Herschel Schachter traced the development of this practice through the Geonim and Rishonim, and concludes that it has a mere status of hefek. Thus,
If it is a mere hefsek, a pause, then it stands to reason that one can (and should!) change what is publicly read into the microphone, so long as the ketuba itself is written properly, and the eidim and husband understand what is really going on. See Shalom's answer for an example of a Gadol, Rav Yaakov Kaminetzsky, who would read a dummy kesuba. The statement of the "seasoned moreh horaah" who said, "who says that what's written there is what you have to read?" reflects what I have heard as well.
For a practical example of someone who recommends changing the out-loud reading of a ketuba to avoid embarrassment to the kallah (though the example is to not read a specific name), see Minchas Yitzchak Chelek 5 siman 44.
Note that the witnesses and the chassan should know what they are signing and agreeing to. Of course. I don't know that "Our modern custom of reading the Ketubah comes from two primary halakhot in the Shulhan Arukh", that Rabbi Michael Tzaddok writes, is correct, and would like to see some concrete support to that speculation, contra the position that it is a mere din in hefsek that sparked the practice.
Especially since I've quite often seen the ketuba signed not under the chuppa, but at the chossan's tisch, and yet the ketuba is still read under the chuppa, we see that all it is functioning is a hefsek.
In those places where the minhag is that they also sign the ketuba under the chuppa, then perhaps there is a fear that the groom and witnesses will mistake the contents of the ketuba, such that a deliberate misreading would not be appropriate. I would like to see a written source of e.g. Rav Ovadia Yosef saying this. Which apparently there is, but I would like to see it inside before editing this post to include it. I would also like to see why the groom and witnesses cannot be instructed as to this portion of the ketuba contents off-mike, so that every gossip in the audience is not privy to the sordid past of the kallah.
To intentionally read the Ketubah errantly is problematic. Our modern custom of reading the Ketubah comes from two primary halakhot in the Shulhan Arukh:
Choshen Mishpat 45:2
Even HaEzer 66:13
Thus we also rely on an accurate reading of the Ketubah to obligate the husband in what is written within it.
Intentionally misreading the Ketubah then would cause very serious problems halakhically. However that is not to say that we are not concerned about the possible embarassment of the bride.
Rav Benayahu Shmueli writes in his sefer Kavvanot of the Chuppah in the name of Rav Ovadia Yosef(sourcing Yabia Omer but not giving volume and chapter):
In my experience and from testing in the Israeli Rabbinut this is the general custom of Israel.