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OK, so that means I cannot underline links or else we create a major game of "confuse the visitor." What we've done, which seem to work pretty well, is make links bold and in an accent color, with a hover behavior that reverses the background/foreground colors.
That creates several areas of redundant clues that scream out "this is link" and the underlined words no longer look like they are links. At worst, one or to tries nd the visitor gets the idea, I think. At least there have not been any complaints, and the site stts look good.
As long as the non-underlined link meets this criteria, you are fine: [w3.org...]
This may mean using bold or italicized text, a border, different font, or perhaps (if using only color) a background/font color which is contrasting enough. If the color difference is there when viewed in 16 colors, you should be fairly safe.