Touchpads are built into laptops because they're thin, but you can get an add-on touchpad that plugs into a USB port on your desktop. Amazon has a few. Here's an example of a basic model similar to what's in a laptop.
![touchpad](https://cdn.statically.io/img/i.sstatic.net/QnVwV.png)
It isn't clear what mouse action leads to your index finger cramping, but a touchpad might not be any better than a mouse because you use your finger for everything, especially if you tap rather than use the buttons (although you could switch to a different finger).
You may just want to experiment with different pointing devices to see what works best for you. Try a touchpad. If you've used one on a laptop, you already know your experience with it.
Another commonly used option is a trackball. There are lots of models. I happen to use this one. (At one time, I used the touchpad above.)
If you have ready access to a computer store (or other store with a big computer department), they may have a lot of pointing devices on display. Try them out to see what feels comfortable. It may also be good to have a couple of different pointing devices. If you find that long-term use of a particular one causes a problem, switch to a different one for awhile.