Chris used a collated text; largely Child' example A (from Scott's Minstrelsy) with parts from the other examples. Scott has "redding kaim", and glosses it as "comb for the hair". The verb to redd means to prepare, make tidy, disentangle, groom (the hair), and so on. Related to the more common rid. A redder or red-comb is of the large-toothed variety.

I don't know that "wedding knife" has any special meaning beyond perhaps being a knife used at a wedding and kept for sentimental value.