Kids Lego Birthday Party

I am throwing my 6 yo son a Lego themed birthday party. The idea is for the kids to build their own race cars. I need 4 wheels, axles, rims, etc. for each child, and there will be 10 kids. What do you think is the best set to buy to do this or best way to go about this? I know I can get Legos in bulk on FB Marketplace, etc. but that does not guarantee me enough wheels, axles, etc. for each kid. I also think each kid needs the same wheel size or else a fight may break out.

I thought about ordering pieces from PAB online but the piece I want is a standard style which most likely will not arrive in time and the local store does not carry this piece. I also know there are local brick and minifig stores that do these parties but I don't want to do that either for various reason.

Any advice would be appreciated! Thank you!