Based on a few examples, it seems [w] vanishes before [u] in Old Noldorin, in the same way as that [j] vanished before [i]. Since the combination [wu] did not normally occur in Primitive Elvish, this phonetic development only applied to cases where the [u] arose later, such as when [oi], [ǭi] became [ui] in Noldorin:

• ᴹ✶wāyā > wōia > ON. uia > N. ui “envelope” (Ety/WAY).
• ᴹ✶wā́yārō̆ > N. Uiar, a Noldorin name for Ulmo (Ety/WAY).

Based on the examples above, this sound change occurred at the Old Noldorin stage, and before initial [w] became [gw]. There seems to be one other peculiar example of [w] assimilating to a preceding [u] in Old Noldorin:

• ᴹ✶kukūwā > ON. kukua (= [ku]kū^u̯a) > N. cugu “dove” (Ety/KŪ, EtyAC/KŪ).

The Quenya form was also ᴹQ. kukua, so the assimilation here might have been in Primitive Elvish, from *kukū + suffixal -wā. But more likely it was a parallel sound change: see the entry on how [j], [w] often reduced between vowels in Ancient Quenya.

Conceptual Development: There is no clear evidence of this sound change in either Sindarin or early versions of the language, but since [j] vanished before [i], it seems reasonable to assume something similar would happen to [w] before [u].