The short answer:
6.5cm to 6cm I would run it through a FL size die with an expander ball and don't think twice about it. Easy peasy.
The long answer:
As you neck down, neck wall thickness theoretically will increase. As you neck up neck wall thickness will decrease. Assuming the case doesn't grow or shrink, you can use the cross-sectional area of the "before" to get the OD radius of the "after".
C/A = pi*(Ro^2 -*Ri^2)
Ro is the OD of the neck divided by 2, Ri is the ID of the neck divided by 2.
C/A before = C/A after
ALGEBRA TIME!

Pi* (Rob^2-Rib^2) = Pi* (Roa^2-Ria^2)
Drop Pi from both sides
Rob^2-Rib^2 = Roa^2-Ria^2
We know the ID of what we're going to (mandrel/expander/bullet diameter) so to find the Roa (radius of the outside "after") just add it to both sides and square root the whole thing.
Roa= SQRT( Rob^2-Rib^2+Ria^2 )
OD after = 2* Roa
Rob = .146 <---I made that number up as an example
Rib= .132 (this is .264/2)
Ria= .1215 (this is .243/2)
then Roa= .1366
So where you started with .014" neck wall thickness (Rob-Rib), you would theoretically end up with .0151" neck wall thickness after stepping down to 6mm (Roa-Ria)... .001 difference wooo big deal.
That all assumes that your cases don't grow in length, too. If they grow length-wise, then whatever volume of material flows up the neck will not contribute to increased neck wall thickness. Depends on lube, die design, etc.
At any rate, with the diameter reduction of only ~8%, you probably don't need to worry about annealing until after several firings.