I have had both of those tools and really gave them a fair shot. I also had the axle bender you whack with a hammer. I can absolutely say with certainty that you can be faster leaving the wheels alone. Just pick through a pile of them and look for the wheels with the least runout. Polish the bores and hubs and race them; but do not take my word for it. Check for yourselves. I did not believe it either and had to prove it.
If you want better wheels, buy them as suggested. I have heard the debate on build the car completely for the experience with your children, but, there are so many other things in which can be done together without spending countless hours trying to enhance a wheel's speed through the use of inferior tools. Aside from the woodworking aspects, sanding, painting, lubricating, tuning, etc., spend time doing some simple science experiments. For example, I typical do these three things:
1. Use a leaf blower to show wind resistance by having the child position his/her hand in different orientations. Let them determine what the body shape should be (thin to win).
2. After jacking up a car, spin a car tire vs spinning a bike tire. Ask which one is harder to turn and why?
3. Have the child jump off a chair. Then suggest they jump off the roof (most kids will not want to do that but some may be more adventurous). Ask them why they will get hurt jumping off of the roof vs the chair. Relate that to weight in the front of the car vs weight in the back.
4. Use ice and sandpaper to discuss the importance of a smooth surface and friction
As far as legality in a race, if they allow you, the parent, to lighten and/or modify the wheels, then you are allowed to buy them. Right now, I could modify a wheel using a lathe (albeit, it would be a horrible job). I could also find someone I know to do it. BUT, some may also need help cutting out the body of the car, or with polishing axles. Why not seek help to true up wheels? Or, why not just buy them outright? Many buy weight (tungsten), something I could never make at home. Why not buy wheels if we are buying other parts? I see very little difference between modifying a wheel using the wheel shaver, modifying a wheel using a lathe, and buying them outright.
There are so many other ways to spend that time with your children than shaving wheels and the money you save on the shaver and hub tool can be used for trued wheels (not the $50 ultra light wheels, but just some simple trued wheels) or just polish and race them out of the box. It really is a better use of your time and money.
Best of luck in which ever way you choose - its just my 3 cents (which is 1 more than 2, another bargain

).