Reading through, they say the finish is self-levelling, and don't talk about polishing. If you want more of a shine than you currently have, as it does look smooth already, then I wouldn't sand at all, just go straight to some fine polishing compound. But rub slowly and keep moving the area you are working on to stop heat build-up. They talk about burnishing the ageing finish with standard photocopy paper, rubbing it to build up heat, to take the edge off the shine. But to polish it further, the finish does need to be as hard as possible, and apart from UV cured finishes, almost all other finishes take at least 2 weeks to get hard enough to get and take a good polish.

The finish must be based on a polymerising oil, like boiled linseed or tung, along with some other additives. So it should harden in a generally similar way to those oils do (also in related products like Tru Oil).

But if you want to put it together to play, and really can't wait, then do so, and then take it apart again in a month or so. I'd start on a small bit of the rear, before dismantling, just in case there's something strange about the way the finish responds to a polishing compound, so that at least it happens to a bit you won't see much and you don't take it apart if you don't have to.

You may always come to like the finish as it is in the meantime!