A SS specific bike is likely to have a narrower rear spacing than a geared road bike, 110/120 mm vs 130 mm for newer stuff.
You can get a freewheel rear wheel and mount a SS freewheel instead of the multi-geared one. Might need to remove some spacers and move some others around to get the chain line good enough. Ideally also redish the wheel.
Cassette hubs can be turned into SS hubs by disassembling a cassette, picking one sprocket and replacing the rest with spacers. I think there are also SS kits sold incl sprocket and spacers. If such a wheel would fit your dropouts.