You don't want a camera with a 2mm lens. you're not trying to use it like an eyepiece and get parallel light rays coming out of the back of the lens - you need something that will focus the image of the spectrum on the camera sensor.

The normal way would be to use a standard microscope USB eyepiece camera without a lens, and adjust the focus of the telescope so that the the image of the spectrum is focused on the camera sensor (i.e. further out than normal), instead of at the crosshair. However, you might end up needing to remove the crosshair if it causes a shadow problem on the sensor. But I don't know if the telescope focuser has enough in focus to get the image far enough out to focus past the end of the eyepiece holder (which is where the sensor is likely to be positioned).

If you could find a camera small enough to slide into the eyepiece holder tube, then you'd have the option of removing the crosshair and sliding the camera in so the sensor is where the crosshair used to be.

Alternatively, you might be able to try a digital camera with a very close focus macro capability, take the eyepiece out, and focus on the crosshair.

Or, you could just try afocal photography - set the camera/webcam to infinity focus, and line it up with the eyepiece lens. This usually needs a camera where the camera lens is smaller than the eyepiece lens - so a phone camera might work well. buy a cheap phone case, and glue a tube that's a snug fit over the eyepiece/eyepiece tube to hold it in the right position.

By the way, if you have a search around, there is at least one shareware spectrographic program (originally intended for astronomical use with a diffraction grating, webcam, and spacer) that may be useful for what you want to do.