I spent a little more than 3 years teaching high school in the mountains of the Gulf Province between '98 and '01. Although I never hiked the Kokoda, I spent a lot of time trekking in other areas. So, my advice is specific to the situations I encountered and may not apply to the Kokoda, but at least it's something to go by.
The biggest difficulty I had on my treks came from the slickness of the hard packed clay, and all the muddy mossy log crossings. I fell more on a typical New Guinea hike than in 50 snow and ice slogs back in the States. You had to be careful, because new growth on a trail's edge is often cleared using downward swings of a machete, which gives the trail a lining of upward-facing daggers. Several times I caught myself just short of being impaled. If I were to go back, I'd take along some sort of pair of micro-spikes. The trick would be to get extra traction without tearing up the trail.
I think you'll get along fine without a guide. It's a very popular trail, and I'm sure there will be no shortage of people to point the way for you. You'll have to change your way of thinking, though. In PNG, the biggest trails often lead straight to the garden. So, the most traveled path will often be the wrong path.
I'd travel as light as possible, and forget about the tent. You'll meet some of the friendliest people on earth. You'll find places to stay, just make sure you offer some cash in return. PNG is a very expensive place. If someone gives you rice or tin fish, or some kerosene to cook with, you can bet they paid more for those items than you would have at home.
Have a good time. PNG isn't the easiest place in the world to travel, but that's what makes it among one of the most rewarding. You'll have experiences that can't be duplicated anywhere else on this earth.