Here's a better option - just buy a track hub and do it properly.
Seeing as this is the Retrobike forum all fixed wheel bikes should be either:
1. Really old fixed wheel bikes from the vintage category.
2. Proper track style frames with rear facing dropouts, fag paper clearances, single brake and drop handlebars like clubmen used to ride, and some still do. All right two brakes is OK.
On no account should any classic Italian beauties or British 753/531 masterpieces be subjected to the kind of botched "conversions" that make a dog's dinner out of decent bikes.
Oh and while I'm on a rant how about absolutely none of those trendy, poser boy new build fixed wheel bikes with flat bars.
As for "single speed" I grew out of that when I got my first real bike. That was a Raleigh Shopper with 20" wheels and a Sturmey Archer 3 speed hub gear.