DS vs DS lite has 3 main aspects.
1) Original DS has comparatively dim screens.
2) Later models of original DS can use variable screens to almost be like a DS lite if you flash their firmware with the hacked one.
3) DS lite screens.
I doubt you will need anything like passme compatibility. If you are 3d printing things then you can probably dodge any concerns with the DS lite having a smaller GBA slot. Sounds like you have already dismissed a DSi or anything in the 3ds side of things. Possibility of an emulated device -- I imagine you could probably smash an android or raspberry pi a like board into a case and grab one of those save dumping tools popular a few years back before tweaking it to work on such a device (I don't think we even saw Linux versions so that would be some software efforts).
Concerns in the general form.
1) hinge button. When you fold the touchscreen in it is not a sleep mode as some assume but actually a button press, some games do use it as such (Warioware being among the more notable). You can fake it by waving a magnet around, which also means you could sub in a switch.
http://problemkaputt.de/gbatek.htm#dskeypad
It does also mention a debug button.
2) Accessibility for DS slot. You could step the DS slot part in the case, you could angle it, you could make a simple redirect board, you could hard encase a DS flash cart and use wifi, you could hard encase a DS flash cart and have some means of attaching an external cable (whether allowed by design or you bodge one together from a SD reader is a different matter, the by design set are not great flash carts through by and large and will not play all the DS games without serious extra patch work).
On 3d printing. Yeah I doubt you get will get much from a conventional extruded nozzle that you care to use for this, though with a decent acetone wipe (and compatible plastic) and thick enough might yield something. Photo curing or laser sintering is a different matter and should be available from the various rental services. Injection moulding would be nice but expensive as you kind of have to make a mould which unless you are already very good is probably going to need a few prototypes, in which case take the CNC setup you would be using to make those and feed it the block of plastic instead -- very few tapped holes, undercuts or similar needed for DS stuff.
I doubt very much you will find a compatible device/shell to sacrifice for these purposes (most times you see that people custom designed a board to fit, and it is not a thing designed to be held for pleasure). You might be able to twist it and bond a minimal amount of DS case (enough for say the holes to all line up) inside a more general block without it feeling like one of those clip on shells.
You would also open the doors for better audio amps, control remapping, turbo buttons and the like.