Your pump is one of the easiest to make new skins for because there is very little taper. You should be able to use straight rolls to turn the curve in the skins then trim to fit.

Your pump should have a cast iron door and frame near eye level. If there is another smaller tin door lower down about knee level it likely uses the handle that pulls out. The little door should have furniture type hinges. Most of these pumps I have seen do not use the normal handle sticking up on the side, but some do.

Does the pump have a globe holder on top or a bar wit two lights coming off the middle above the top bonnet??