Hey CaptainKiran,
It's up to you for the bracer.
Building upon something like that cardboard tube will be easier - since it's the same circonference all the way around.
But then, I think it will make it look funny - since the pipboy is really built on a cone-like shape for the bracer to follow the contour of your arm... and yes my forearm is definitely bigger than my wrist as well
How I did the bracer: like I always do for new costumes/props... I make a pattern out of cardboard and them cut it up in foam.
I wrap a cardboard piece around my arm... and marked it where it overlapped... and cut it up and I had a pattern for a truncated cone that fit my own arm. Then I copied the same pattern to another piece of cardboard and cut it up for the different raised parts on the pip boy bracer. So when I was all done, I had a cardboard piece cutout for every piece I needed to cut in foam to assemble the bracer... easy-peasy
Be careful if you do something similar... if your foam is thicker than the cardboard you're using for your pattern - you'll have to cut your foam piece a little bigger than your pattern to take into account that difference in thickness.
As for the back of the pipboy... find out where you need to glue it to your bracer and carve out the foam so it sits right on the bracer - then hot glue it in place. As simple as that.
Just a suggestion - don't overthink stuff... try it out and see how it looks.
It's the whole point of working with cheap stuff (foam, cardboard, hot glue, etc.)... if you don't like it, scrap it and start over... cardboard is free since everyhting you buy is always packed in a cardboard box - save them and make patterns with them. Foam sheets can be had for less than a 1$. As I said in an ealier post - you can easily put this together for less than 20$ if you have to buy everything (foam / paint / glue / etc.).
Good Luck !