For the Ninja V, there are currently two categories of commercial option available - buy an empty sled from Atomos and install your own 2.5" SSD or buy a smaller AtomX SSD for twice the price from someone like Sony or Angeldisk.
The bummer with the sleds from Atomos is that a standard 2.5" SSD is long enough that it sticks out past the edge of the recorder and looks bad.

There are some other models on thingiverse which do something similar, but one is for Samsung SSD's and the other involves sawing the drive in half.

I have a few ~500 gigabyte Sandisk SSD's and from what I can tell, they all use the same PCB layout which only takes up about 1/3 of the total space inside the 2.5" case. I'm not sure about smaller models, but the couple of 1TB Sandisk SSD's that I have use a full length layout so there would be no benefit to extracting them.

Note: THIS WILL VOID YOUR WARRANTY and may damage or reduce the lifespan of your SSD. I take no responsibility for this - I'm only providing the model if you choose to do it.

To use it: peel the white sticker off the bottom of the Sandisk SSD and unscrew the 4 screws that hold it in place. Gently peel it away (the side with the screws is metal and is used as a heat sink by the drive in normal operation - so it's stuck on with a thermal pad). Inside, you'll find a short circuit board with the SATA port on it that is held in with 2 screws. Unscrew it and remove it.

The print has holes for each of the screws and a backstop for the circuit board. The screw holes aren't perfect, but on mine, the screws stick in it well enough that (combined with the backstop) the circuit board doesn't go anywhere. After you have the drive mounted test that it fits right in the Atomos and doesn't have any play with the retention flanges. Then remove it, put a little super glue on the lid, and it should snap in place. Wipe off any excess glue and let it dry for a little while.

To (hopefully) avoid overheating and reducing the drive's lifespan (and prevent performance problems), there are a few vent holes in the model which will hopefully promote some airflow. This means that the part is absolutely not weather-proofed (though neither is the Ninja V with its fan holes).

How-to video:
https://youtu.be/GevDjsoDC_A