You should be able to use the direction pad to change what your Y button is assigned to. Left direction will equip pistols so that Y becomes shoot. You may need to progress in the game first if you don't have any other items to equip. I have barely used the other items and I am about 45% complete.
I got this game bundled with the XB1. It took a lot of time for me to get into this game, but now that I have, I am enjoying it. I had to run/sail around and explore the map for a while before I could upgrade the Jackdaw and progress with the main mission. The last AC I played was the first one on 360.
Good luck!