Remember that we are making the rash assumption that your's is the same as mine!
When you remove the 'C' clip and the pinion gear, the woodruff key will become a non-issue. Toss it too, as your goal is to make this a manual push with no resistance from legacy hardware.
My experience with lithium greases is that they dry out. Wheel bearing grease should be fine, but keep the coat light. The really heavy greases (I once made the mistake of using Husquvarna gear box grease!) can seem like you've used glue. I've also thinned grease with a tiny amt of light lube like a penetrating oil. Probably NOT the recommended procedure, but it works!
The round sleeve in the wheel that the shaft passes thru is either a sleeve bearing (cheap mowers) and that's what spins on the axle, or it's the interface between the axle and the wheel with a set of ball bearings hidden in there. If you can spin that sleeve within the wheel, you've got ball bearings hidden in there. You'll likely be able to induce some motor oil or similar heavy lube to pass between the outside of the sleeve and the wheel to lubricate those bearings. Wipe it down well first, and you should see a tiny gap for getting some oil in.
As an engineer, my gut feeling is to trust the judgement of my fellow engineers - the guys that designed and built this mechanism. They might not be always perfect, but I believe they know what they are doing. So when they said grease, they probably meant grease. If you deviate, you do so at your own risk. The bushings on both sides of the pinion, when combined with sufficient grease, seem to hold a reasonable seal and keep dirt out. I don't believe a dry lube would protect the spring loaded woodruff key, key slot, and inner eccentric mechanism as well as a light wet lube. But hey, that's just my feeling on this. Do as you see fit.
For this application, I used Park Tools Polylube 1000 - the same stuff that protects the small bearings on my bicycles and other systems that call for a high shear strength light grease.
True, the exposed gear teeth might benefit from a dryer lube to keep from attracting too much fine dirt, but the one-way drive mechanism should be lubed as prescribed.
Bert,
I did read the owners manual many years ago. While I didn't remove the wheels, I did give them each a shot of motor oil each year and clean around the height adjustments. But, that's all other than changing the air filter, spark plug, and I did change the oil once. It just keeps on runnin. Years ago, I was going to fix the self propulsion, but, then decided it was the only exercise I got at the time. So, I just kept on pushin.
If and when I get a new one, I will definitely maintain it better, now that I'm retired.
I also have a 99 craftsman lawn tractor my daughter gave me 10 years ago. I use it to do the back yard. Now that thing keeps me busy with maintenance, greasing, oil changes and leveling the deck. I bring the battery in each winter and put on a trickle charger. Deck removal I've done once. What a PIA that was. And putting back on was a challenge. Come winter I'm going to remove the deck, bring the deck indoors, and coat the deck with rust inhibitor and then paint. The thing looks terrible, but, starts and runs with one turn key each time. I also keep it outside, covered with a tarp. No room for it inside.
Well, thanks again for your thoughts and suggestions. I appreciate it.
John