How to get the two "Statuette" quests done?

Solution 1:

Triss can help you with the statuette quests. It depends when you find them, but before the battle of Kaer Morhen you can talk with Triss and she will help.

To update - there is a time after battle of Kaer Morhen, when she is freely available to just talk and not in the middle of any quest. Also, you can talk with her after the main quest line ending, then she will help to decompress the statues.

Solution 2:

After playing it, here's why I got:

I had to wait until immediately after the quest "A Poet Under Pressure" (last quest of the Novigrad quest line) before being able to progress in "The Nobleman Statuette".

After that I could progress in "The Soldier Statuette" after finishing "A Dangerous Game", in which you usually get the statuette itself. But I still had to wait for the "A Dangerous Game" quest to be finished before completing "The Soldier Statuette" quest.

Important information: Triss' path was NOT started.