A noun for “nail” in The Etymologies of the 1930s derived from primitive ᴹ✶taksē under the root ᴹ√TAK “fix, make fast” (Ety/TAK). Here the k became spirantal before s [taχse] and then vocalized to i to produce the diphthong ai [tais(e)], which then developed into ae [taes].

Neo-Sindarin: These Noldorin developments of the 1930s are different from the spirantal developments of Sindarin of the 1950s and 60s. It seems that ancient ks became ch in Sindarin: compare S. ach “neck” from primitive ✶aks (PE17/92). If you update this “nail” word to fit these developments it should become ᴺS. *tach. However, I prefer to retain the 1930s form taes and assume it was a dialectical variant.