I cannot speak with authority on this subject, but I can make some educated guesses.
The 1806 shako was only authorized in 1806. Some units might have seen them as early as 1807, but I would expect it was not until 1808-1809 when they were common, EXCEPT for units deployed to Spain, who may not have been refitted before marching into Spain.
I would expect that the 1810 shako was common by 1812. Units in Spain would have seen them arriving, perhaps without ever seeing the 1806 model. Units in Europe would have been replacing their 1806 shakos in the wake of the 1809 campaign.
If we could get to the army records at the Chateau de Vincennes, we might find logistical records of them being received by various units. But that is Scotty Bowden territory, and I doubt he would spend his time at Vincennes researching such trivialities.
As for miniature figures, I don't know that you could tell much difference.