You indicate that both these sentences refer to talking style. However, tbe use of 'wording' is suggestive of written style. A better way to express the second sentence (for talking style) is, he speaks in a conciliatory way.

The first one is fine. For the second one, I would say "he uses conciliatory wording" or "His letter has conciliatory wording." People "use" wording, they don't "have" it. "wording" is also uncountable, like air or water. The meanings are very similar, but "wording" emphasizes his word choices, while "style" would include his grammar patterns.