Cyanotype is generally not a practical choice for a pinhole camera. Its light sensitivity is very low, so exposures would likely be extremely long. That means you’d be limited to very still subjects, and anything moving during the exposure could blur or disappear.

A more practical option is ordinary silver-halide darkroom photographic paper. It’s commonly available, works much better in simple pinhole cameras, and is relatively straightforward to process. You will need a darkroom or very dark space and ideally a safelight, but handling and processing are usually easier overall, especially with resin-coated paper.

So: yes, cyanotype might respond to light, but for a homemade pinhole camera it’s likely too slow to be effective. Standard photographic paper is the better beginner-friendly choice.