I do have some experience with the particular calibration tool in question, and while it's hard to give a general answer to questions like "Is paper an ok diffuser?" (there are many kinds of paper), I'll share my experience.
Firstly, I feel a little differently about the importance of calibrating vignetting at different focus distances than what Torsten expresses in his tutorial. My experience with the lenses that I own is that they have stronger vignetting when focus is at infinity than at closer distances. The implication of this is that if you only calibrate at infinity, close shots will be over-corrected.
In my opinion, over-correction of vignetting looks terrible, both because it looks very unnatural compared to the "problem" that it's supposed to be correcting, and because it tends to pull up noise from shadows in the corners (where the correction can typically be as much as 2 stops for wider lenses). I gathered from personal correspondence that the reason for downplaying the importance of multiple distance calibration in the tutorial is in hopes of making the task less overwhelming to anyone considering it, but I would say that it's well worth doing at least MFD and something around 2-6 times that, unless the vignetting is clearly very similar at both ends of the focus range.
If you really want to only take images at one focus distances (perhaps for a manual-focus lens that doesn't produce EXIF information about distance, or a camera system where the distance reporting is unreliable) it's probably best to calibrate for the least case, wherever in the range it occurs.
Now as to the actual question about methods of getting an evenly lit calibration shot... it's complicated. I've gotten good results using the diffuser-in-front-of-the-lens method for some lenses, and not others. In general, it seems like the wider-than-normal lenses can produce calibrations that, when applied to real-world images, result in the aforementioned horrible icky over-correction. I don't know exactly why this is the case, but for those lenses it was true for all the different diffusion methods I tried. The main point being: check your results on some real-world images that will easily show this, at different focus distances.
In the cases where this method did give good results, these were obtained by making sure that the diffusion material was held tightly against the face of the lens by something flat (such as glass), so that no light can "leak" at the edges. Eventually when I obtained a device with an OLED display I found that setting the lens on a sheet of diffuser on top of a full white screen worked as well as anything I had tried previously, but DO NOT do this with backlit screens - they are not reliably evenly illuminated. Otherwise, the diffuser can be lit as described in the tutorial, by pointing at an evenly lit ceiling. Extremely ambient lighting is best, it doesn't need to be bright, long exposures are fine...
...which brings me to the part about those lenses that didn't seem to give good results with this method. For those, I ended up pointing the lens, without a diffuser, at a very dimly, evenly illuminated ceiling, such that the exposures lasted a few seconds, and rotated the lens around it's axis during the exposure to further average out any uneven lighting, trying for roughly one full constant rotation during the exposure. This turned out to work quite well, and the dizziness wore off eventually. :D
As for the diffusing material, I tried various things I had around, which included some Roscolux diffusion gels. That stuff works great if it's in pristine condition, but it can easily get scuffed in ways that make it unsuitable. I've also found that multiple layers of LDPE sheet (available in many craft stores) can also give very good diffusion. Probably some types of paper can, as well, but some are surprisingly "blotchy" when held up in front of a light. The main thing is to check whatever you're considering using this way, to make sure it isn't contributing any uneven distribution of the light. I would probably also reject light tables as a direct light source, since they probably don't have the critically even illumination needed (taking a photo of it might reveal this).
So, that's my brain dump. One other thing worth mentioning is that the script depends not only on python, but also some hairy math libraries that you'll probably need to install somehow, so be prepared for that.
ADDENDUM: I had a reminder today about how image stabilization mechanisms can produce variations in vignetting. This needs to be disabled for the shots.