You are thinking of a fixed gear bike. Most single speeds are still a freewheel style bike meaning when you stop pedaling the rear wheel keeps turning without the pedals moving (has to do with the style hub). A fixed gear bike, still a single speed, uses a different rear hub so if the rear wheel is moving so is the crankset. Not something I would recommend to your basic cyclist.I have ridden a bike like this before, if you get going down a hill you have to stick your legs out to keep the pedals from hitting the back of your legs is this correct? Maybe you could get a tire off another bike similarly sized and slightly bend the back frame mount area outwards/inwards to fit it
Never try and bend your frame in or out to fit a different wheel. Your frame was designed for a specific wheel and shouldn't be modified unless your willing to risk damaging your bike, or yourself
to the OP, if you are just gonna adjust your limit screws to make it a SS why not just ride it as is and dont shift? You could possibly use your rear wheel if it is a cassette and not a freewheel style. You can just break the cassette apart and get some cheap spacers from your LBS and put one cog back one. The front will be a little trickier depeind on the crankset you have. Let us know and we can help you out i am sure. Good luck