I wonder if it was this one off
eBay, given that it is your size?
That should make a very nice SS.
I converted an old steel-framed Basso into my SS. All I had to do was to take bits off and then I got hold of a load of spacers and took all but one sprocket off. A bit of trial and error gave me a perfect chainline. I used a 39 chainring with a 15 sprocket. Here's a picture of the end product.
And here's how I fixed the sprocket in place...
I did a test ride with the bike set up like that and the chain came off the sprocket twice in about 3 miles. I concluded that this was because cassette sprockets are designed for it to be easy for the chain to move up and down the cassette. Not so handy when there aren't any other sprockets...
So, I used a bit of lateral thinking and put bigger sprockets from the old cassette either side of the one I wanted to use (after the second photo was taken). They act as guards to stop the chain coming off. The bodge works perfectly. I've ridden hundreds of miles on the bike since then and the chain has never come off again.
Even though my SS has a steel frame/forks, it was surprisingly light once the redundant bits were taken off. I haven't weighed it but I'd guess it is about 19-20 pounds.
I can feel how much more efficient the perfect chainline and lack of jockey wheels makes the bike - it is really easy to spin those pedals round. The gear I chose is perfect for me at about 20 mph (cadence of 100 rpm). I start to spin out above 24 mph (120 rpm). It's okay on shortish hills up to 7% or so, but I don't like long ones or steep ones in that gear.