You don't need to move it relative to the skycamera... they are already aligned at regular size before being shrunk (spatially).
As i said: place the skycamera at 0 0 0 and the skybox rocket nose model where the regular rocket nose model would stand (origin, that is). Select the skycamera and the skybox rocket nosecone model (readily aligned to the regular sized one) and shrink them -rocket and skycamera, together- on all 3 axis, by 0.0625.
Your rocket nose cone is aligned at 1/16th scale.
Why is this hard to understand?
The only way they would become misaligned is if you touch the 3dskybox contents after this process, or move the maps orientation to 0 0 0 after completing this process.
Edit: Or another way of saying it. Shrink the skycamera placed at 0 0 0, with the regular sized nosecone model, so spatially they are at 1/16th scale, then swap out the regular size model for the skybox version. (saves you overlaping the large and skybox versions) but the process is the same. The important thing is that the model origin and skycamera are aligned. Grid alignment doesn't matter in the 3dskybox and only becomes a problem if you start moving stuff around in it seperately.