First... I would really think about how practical a case like this is going to be for you. I prefer to use racks, because once a pipe goes out of my sight, I forget all about it. A regular 2 or 3 pipe case can at least also hold some tobacco and pipe cleaners, maybe a lighter and a tamper. These fitted cases don't hold shit but the pipe. So, most likely, you are still left with more baggage outside of the pipe case. Are going to have a fitted case made for your lighter and maybe one for your pipecleaners as well?
A meerschaum... I can see needing extra protection, because a good bump can flake off a side or just crack it. They are practically plaster. But a briar? No.
Once you've truly considered how impractical a case like this is, besides just looking neat... and you still wanna do this.... maybe consider some alternatives.... using paperclay from your local Hobby Lobby shop, which is a moldable paper based paper mache product that sorta acts like clay in the way you work it, except it air dries.
Maybe conder using Sculpy, which can be baked hard in you oven at low temps.
Old luggage used to use paper mache, which is sturdy up until you get it wet.
Then, to cover it... take some leather working classes at the nearest Tandy Leather store, get some skillz, take some classes, maybe try making a wallet or a belt first, then tackle stretching that hard to work shit out with your strong bare fingers. Leather can be too expensive to just start improvising with it (making it up as you go along). Or, maybe use vinyl faux leather and a heat gun. Then add some stretched felt to the inside.
And... unless you get lucky or have a real knack for doing arts and crafts, your first four or five are going to look like total crap. Making hinged objects is usually not a beginner woodworking project, because hinges presents some real 3D challenges for folks that don't think in 3D like this.
Of course, this is not rocket science, nor is it a complex cabinetry. But, really, you have to ask yourself how much you really "need" something like this.