One does not run into a lot of references to this sort of thing in primary sources. This either means that there weren't a lot of tattoos or people weren't discussing them. I suspect there were far fewer tattoos than today (there were far fewer tattoos forty years ago than today!). And I suspect people weren't discussing them.

There was an "exhibition" of "Fiji natives" that toured the west in the 1870s, and one finds descriptions of their facial tattoos. Some Native Americans had facial coloring of various sorts including those resulting from tattoo-like methods. These inkings received some comment in primary sources - and they are described as unusual, which gives us a hint about how most people did not have them.

You're asking more about those who came to the West as settlers of various sorts. I have not seen a description of facial tattoos other than as you say someone who had been a Native American captive. One can only infer the lack of facial tattoos by the reaction of the few facial tattoos that are described - Fiji and Native Americans - deduced as rare based on the descriptions of that ink as a curiosity.

I'm helping to transcribe and annotate the full journals of Alfred Doten (1849-1903) who came to the American West as a '49er and eventually became a journalist in Nevada. On January 7, 1857, he wrote the following:

Evening I pricked in some Nitrate of silver into the name on my left arm to eradicate it

The annotation I wrote about this is as follows:

Doten was employing the popular "Variot's method" of tattoo removal. In 1918, Dr. James Peter Warbasse described the process as follows: "The skin is cleansed, and a 25 or 50 per cent. solution of tannic acid is painted on the tattoo marks. This is tattooed in. A stick of silver nitrate is then rubbed on the skin until it is black with silver tannate which is formed in the skin. The surface is then washed with water. A crust forms which comes off after two weeks. A thin pink layer of skin appears under the crust. In the course of a few months this becomes paler and leaves a scarcely noticeable scar." Others attested to the efficacy of this approach.

Sources: James Peter Warbasse, Surgical Treatment: A Practical Treatise on the Therapy of Surgical Disease for the Use of Practitioners and Students of Surgery (Philadelphia: W. B. Saunders Company, 1918) 849; William Allen Pusey, The Principles and Practice of Dermatology: Designed for Students and Practitioners (New York: D. Appleton and Company, 1911) 817.

So far (to date, I have covered 1849-1883), I have not found another reference to Doten having a tattoo - or for any of his friends having them. This single reference to "the name on my left arm" fascinates me: it tells us that he had a tattoo on his arm and it was of the name of someone. We don't know the name. He had sailed to California from Massachusetts and around the Horn, so it could have been a ship's name, but it could have also been the name of a woman - perhaps. We don't know, and yet this brief reference tells us a great deal, shedding light to the elusive answer to your question.