The ones my coworkers have made put different bump dots and things like velcro stickers on the different colours. You want something shorter, so the carpet may not work well. Also, sandpaper stands out as a texture, but isn't something you want to rub against for very long.

Additionally, they have commercial produces ones. Where I work used to sell them, but is appears they don't anymore.

http://www.twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=63

http://www.yankodesign.com/2010/03/17/color-rubik-cube-for-the-blind/

The braille one, while conceptually useful, isn't as practical, because they wouldn't be reading the colour constantly. You can usually shorten it to just two letters.

I was thinking about hacking a rubik's cube the same way a few years ago.
Now I'd just order this http://www.braillebookstore.com/Tactile-Turn--a--Cube.1 free shipping too. I had found some on maxiaids earlier but a lot more expensive.

I think all of those materials would work (eta: except carpet, too tall). Other ideas would be velvet, felt, and plastic rhinestones. Of course, one side can be left plain.

If you want to do raised shapes, I would recommend drawing them with puff paint on wax paper then adhering them with something strong like Gorilla Glue. This will give you more time to make a cleaner shape since the hot glue dries so quickly.

Good luck! You sound like a very thoughtful brother. :)