With all respect to Sheldon, I frequently use his notes and references, I disagree on the skewer but I also see that often on forums people confuse what he really says.
He says that if you have the OLD ALL STEEL skewers and don't want to replace the axle with a solid one, but want to have a simple quick and cheap conversion of geared bike to single speed, you can still use them. If I remember he says that the newer aluminum-nutted/levers are not adequate.
Now, a 10mm solid steel axle and its steel nuts can handle enormous tightening force. The larger the tightening force the larger the amount of static friction caused by the nuts/drop-outs to the axle spacer/nuts. A 3-4-5mm skewer even made of titanium can't handle that much. All steel skewers may be borderline adequate, but you can't find those of the old cro-mol-steel any more and even the skewer shaft itself is not really made of good enough steel as they used to.
I have seen many modern skewers snap from excessive force, from bearings going bad and shafts being bent. On a single speed bike you need all the strength you can get and hollow axles with high powered loads, sprint, starting up hill standing up, can't handle it. Racing velodrome for decades people would know better and use hollow stuff for weight savings. They don't! Some of those riders can take a top of the line 22s race bike, shift in highest gear and really reduce the frame and drivetrain into scrap plastic and alloy bits. It is like putting a train engine power on a 3d economy 4 passenger car.
The damage you will get on the wheel, drivetrain, frame, and yourself when all this fails under maximum load is not worth the chance of being cheap and lazy. Switching to a solid shaft and HD nuts in the rear is priceless security, cheap and quick if you have repacked bearings in the past. Then yank on that breaker bar to 40-50lbxft ?50-60Nm?
Solid axle, gnurly nuts that bite into steel, and a breaker bar, then get a real chain 1/4-5/32 and show that bike who is boss.
PS [Edit] I know the question is old but answers are here for everyone not to personally answer to the one person asking. This is a reference for all those that face a similar problem and it is pretty common.
PS2 How did I forget the most obvious of what I wanted to mention. Modern skewers have nice chrome plated springs inside the skewers to center them while they are released. Most often those springs are wider than a 9-10mm axle and foul up the nut's surface that is meant to hold the wheel together. When the axle slips with those on it is because the nut's surface is making contact with the squished spring against the drop out surface and makes it more likely to slip. Older skewers if they had springs they were tiny, these days because in 95% of applications it is a vertical drop out it is not important and those conical springs are 12-13mm in diameter. Take them off and the skewer will be able to provide more friction. They just tangle up a bit while installing or removing the wheel.