Won't the inside ring of the W-1 hood accept a smaller cap?

I went through a similar problem a while ago with the Nikon HN-15 hood (which looks like this). Because of it's weird shape, the HN-15 won't accept caps on the outer ring, so in the end I bought an 82mm Tamron pinch-style cap which fits on the inner ring of the hood (which is also a weird shape, since it doubles as a series IX filter holder).

The Tamron lens caps are copies of Nikon's, but in my opinion the former are much better made, they come in a greater range of sizes, and are more reasonably priced.