How did ancient Native Americans shave pre-1492?

Perhaps they used obsidian blades which are dangerously sharp as shown here.

They used obsidian, as @gondwanalon said, or they used a sharpened shell. Or a sharpened piece of copper.

They did have the advantage of having finer facial hair than those of Europeans but they still had it. I believe the main method of hair removal was plucking although, facial hair was common in southwestern and northwestern tribes.

Maybe they did not?

Same way ancient Europeans shaved before the advent of metal blades. Sharp stone edges and shell edges. The ancients in Greece and Rome used to use oil and shells to scrape themselves clean before the advent of soap. There are also saponin containing plants that act like soap that they knew about and washed with.