Firstly I would like to note that I own both the PS3 and PS4 version of the game and all DLC and I do not have this problem on PS3, only on PS4!
I do NOT use mods and will refuse any solution that should suggest the use of such!
When I give Kharjo a custom bow, he will either not use bow at all, or only the standard hunting bow.
What I've tested so far:
- gave him a custom bow, arrows and melee weapon and shield.
- result: he refuses to use the bow, doesn't even use the standard hunting bow.
- gave him custom arrows and melee weapon and shield.
- result: he uses the hunting bow when needed as well as melee weapon and shield
- gave him custom bow and arrows and removed the melee weapon and shield.
- result: he uses the custom bow and arrows.
I've tried this in 5 different new games and also did a complete factory reset of my ps4 including the deletion of any existing saves and starting from scratch, but to no avail.
I must say I feel quite let down by the PS4 version as not only have you kept the already existing, and very well known, bugs, but also implemented new ones.
Not a great customer experience nor value for money.