The thin wheels are still available through Royal Racers. Check it out at their website: www.royalracers.com
We recently ran a Royal Racers event at my church and we used the old style thin wheels. There were only six entries If you want to go further running district and national level Royal Racer events you must run the thin wheels.
We'll be running a second event in July in which we'll be running under WIRL rules. I'll have far more entries. We ran stock classes for 1st - 5th graders and stock classes for teens and adults. We had about 57 total entries.
I'm not a big fan of Royal Ambassador Royal Racer racing as its to antiquated. Reminds me of BSA Pinewood Derby back in the 50's If I were you I'd encourage the group who you intend to run with to impliment WIRL rules.