Lucas brand lithium #2 red tacky grease is ideal for lubricating steering sector & pinion gears, available at most auto parts stores, give it a try.
Opinions, almost everyone has them, whereas common sense not everyone is blessed. Running steering sector & pinion gears dry will do more harm than good, depending on use, last a few years. If you do not lubricate annually, metal shavings will appear as well as worn teeth on gears. Some dealers & their mechanics/technicians do not want you to know this because they want to make that expensive repair & your money. Most if not all new mowers with steering sector & pinion gears come not greased, expensive or not so much. If you're worried about dirt getting into grease, purchase or fabricate a rubber boot to cover gears.
Rivets, you should have stayed in the classroom on this one.