You may be hard-pressed to be able to find a term or type of supplier than easily allows you to purchase the refills of the correct length. They're likely specialty pieces being manufactured directly by the companies making novelty products.
However, it's possible to cut disposable refills down to your desired length (as long as they aren't the metal-case refills) using a sharp utility knife.
This DIY Hacks and How-Tos video demonstrates cutting the disposable refills down to size. As you can see from the video, even cutting mid-ink doesn't cause the ink to spill out. There is a little spillage on the tip from the process, but that should be all.
The reason why this works, is because the ink is already prone to staying inside the refill tube. There are 3 main things keeping the ink in the tube:
- The viscosity of the ink. It is thick and does not "like" to flow.
- The surface tension of the ink. It has a high surface tension.
- The adhesive force between the ink and the tube itself.
These all combine to make the ink not want to flow backwards out the tube, even when cut. The surface tension and adhesive force is strong enough to resist the flow of gravity (as seen by the fact that you can buy a pack of point-up pens that have been hanging for months, and there's no spillage). The adhesive force is actually strong enough to make the surface of the ink concave instead of convex (if you've even done the trick with filling a cup with water over the brim without spilling, you'll notice the result is a convex surface).
Since you're only adjusting the length of the refill tube, you are not changing any of the 3 properties listed.
So, you can buy standard refills and cut them to length. Just make sure to clean the ends of both pieces, and properly dispose of the end without the ballpoint. If you'd like, you can also extra the ink from the extra ends to play around with. The King of Random extracted ink from 1000 pens for this purpose. I link the video as extra evidence that the ink doesn't just leak out, even when they remove the ballpoint, but they had to physically push it out with a rod small enough to fit in the cartridge.