Fixed/free hub

Yes, but it'll be a singlespeed and not a fixed gear. It's a good solution, because you can pick your chainline to whatever suits.

Alternatively, if you have a couple of knackered cassettes, take them apart and you will have enough spacers to enable you to just buy a singlespeed sprocket.

But if the wheels are shimano 8, 9, 10 sp compatible i.e. they have that sort of plastic hub-end (the splines shown above) I won't just be able to screw a screw-on single speed sprocket, right?