Chukhchi Guard
Chukhchs were bodyguards of the king. Unlike Tadzreuli, which means guard of the palace, Chukhchi must have been term used only in the royal court because we know that there was a royal title "Chukhchari" which means chief of Chukhchs. Also the King/Queen most likely had both Tadzreuls and Chukhchs because both are mentioned in sources of same period. Probably Chukhchs were a few dozen personal guards of the king while royal Tadzreuls were more numerous guarding the palace, royal family, court and also performing the role of a royal force. High nobles had own Tadzreuls as well.
Me and Khevsur decided to suggest adding the Chukhchs as two handed axe elite infantry and also, if possible, as cavalry which will be only king's guard with 1h axe/lance.
According to Georgian historian Mamuka Tsurtsumia(those links belong to him), two handed axes were spread after contact with Varangians and by depictions we know that viking 2h axe was used at least until 14th century.
Here are guards of the king with axes:
According to the same source, one handed axe was much less popular than swords or maces what was assumed after analyzing several Medieval sources but we do have writings where cavalry hatchets are mentioned, for example: "In 1049, in the battle with Turks Liparit had hatchet"(Stephen Orbelian). So, giving some hatchets to the cavalry is justified.
Their armor should look quite similar to Tadzreuls' armor as Khevsur drew. You could also add lamellar on shoulders and lower part of the body like in the link of Khevsur's last post.
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As you see Khevsur also added nose cover to the helmet of Chukhchi. The thing is that there was some rules in Orthodox iconography. For example Saints never wear helmets on depictions because they have halos. The second unfortunate rule was that the faces must have been open. So, you won't find a fresco, Georgian or Greek, where warrior has nose cover or chainmail mask while wearing the helmet. Although, not every helmet is depicted on the heads of warriors. So, those which aren't, appears to have nose cover and the mask!
Like this helmet is drawn without nose cover in one depiction but in the other the exact helmet of the exact same character is depicted with it:
Here we see that helmets of all warriors are open:
But as soon as the character takes the helmet of the head, phew, it has face mask.
So, adding some early period Georgian egg-shaped helmets with fixed nose cover is justified. Also, some face masks would be ok too. As for late period helmets, we already know that they had nose covers. I suggest Khevsur's links for more info.
Here is in which period you should use each Georgian helmet: