If you are on a fat free diet, you shouldn't be eating brisket anyway. Leave all the fat on. When it comes to flavor in meat, fat rules! It's easier to remove the excess fat after cooking anyway.
I prefer smoking flat in a foil pan, but then I have a relatively large smoker. Laying in a foil pan braises the meat, and that is a preferred method for a tough stringy cut such as brisket.
If you can't fit it in that way, I would think that hanging would be better than cutting it up. Just be sure to catch all the drippings, and I would also have to paint them back onto the meat as often as I was able..
BTW, your sig. says "bait". What do you fish for?