I am assuming you mean Axe from SOH as opposed to Axe from "a bitty fic?" ? If not, I would be more than willing to answer this question again. haha!
Anyway, Axe from SOH:
A bitty reader? A palm-sized wonder? Well, look at that precious little snack. How c u t e.
Axe would find it overwhelmingly adorable how such a small little bean could be like that. He himself is highly a bit territorial, but this is just cute. They could help each other keep an eye on things, hide things, keep others out of their business… It’s endearing to have someone like-minded. He also finds it convenient how easy it is to keep them away from the others in the beginning.
He doesn’t like to share all that much, after all, his Paps being the only exception. A territorial bitty reader would most likely feel the same.
It’s nice having more time with them. He doesn’t even have to be all that discrete with it. Why sneak off to his room when he can keep them tucked away in his shirt? He would absolutely hide them in a pocket or a pouch hung around his neck and tucked securely down the hollow of his ribcage.
Axe would also be more willing to commentate the goings on around them this way, opening more opportunities for casual conversation. It would help them bond a lot faster beyond savior and rescuee. In a way, Axe would become more relaxed and less snappy around others to keep his little treat safe. (don’t want to get into an altercation where reader could get dislodged or smashed…) It also makes him a lot more dangerous should someone else get ahold of reader.
However, Axe wouldn’t be as balanced emotionally with a bitty reader. Like a double-edged sword, he would be calmer with them but more volatile should something go wrong. The stakes would be bigger in this scenario. There would be a more likely outcome for others getting truly hurt.
In short: Axe will be calmer to be around, reader would stay hidden a lot longer, and more mysterious shenanigans would happen around the ship. Don’t tick Axe off. He will be far less likely to hold back…