Day sgian dubhs, or "day wear" sgian dubhs, are traditionally worn with more casual attire for work or play. Antler, horn, and wood are common materials for day sgian dubh handles. No surprise, since these originated as the common man's or working man's sgian dubh, and they worked with what materials they had available.
Today, you can wear a "day" sgian dubh with any kilt or attire you want to. If you want to wear your stag horn or blackwood sgian dubh with a formal kilt and Prince Charle, please do! In general they tend to go best with more casual, rather than formal outfits.