One thing to keep in mind is that cyanotype is slightly acidic and something with a basic PH will make it blotchy or ineffective. Most buffered art paper would be basic. gypsum board would be basic. Probably wall plaster/mud would be basic as well. A PH neutral surface would be best.
The process of washing (developing) the finished would be difficult on a fixed wall. Could you temporarily attach cyanotype coated fabric to the walls, expose, take down and process, and when it's dry, glue it back on the wall with a PH neutral adhesive and modge podge topcoat? Fabric wall covering could be kinda classy.