What you are looking for is a software that can make some kind of stitching.
It's not really a classical projection as those tend to project a sphere into something else (you generally take pictures using a tripod and just rotate the camera, not moving it).
You really don't want cylindrical projections (which are projections from a sphere to a plan) or cubic projection (projection from sphere to a cube). Examples of what you don't want here : http://hugin.sourceforge.net/docs/manual/Projections.html#Cylindrical_projections
What you want is a feature sometimes called "mosaic mode" or "stitching mode" in software.
For example, the software Hugin can do it (http://hugin.sourceforge.net/tutorials/Mosaic-mode/en.shtml). Windows offers ICE, a free tool (http://research.microsoft.com/en-us/um/redmond/projects/ice/).
I think your question is very close to How can I stitch a panorama correctly if I moved the camera along the horizontal axis?, and similar to What would be the right approach to take pictures of a long counter? and Panorama with rectangular projection.
For your purpose, the "best" way (IMHO) to take pictures dedicated to be stitched would be to walk sideways along the wall, taking pictures directly facing the wall (eventually using a tripod).