A Saturday crossing might be more busy, but it won't make a huge difference. It depends more on the people working at the desks and whether you end up behind a bus group!
On the SA side, you will get to a gate, where the police will give you a piece of paper with your car make and registration, amount of passengers. This paper you have to give to the customs officer to be stamped, (and show it to the police at the gate going into Swaziland
) . Then park your car under the big fig tree on the right. If you have big cameras, laptops or other valuables you might have to go into the SARS office first, ask
them if it is necessary to declare your things, they are not eager to give you information!
Then you go into the customs office, show your passport and gate pass, should go quickly. Get in your car, drive to the gate, leaving SA, give your gate pass. Drive through no mans land for 100m, when you see the 'boom gate', park on the right. Enter the little building (Swaziland customs). The guy on the right will stamp your passport and ask your car registration number. He will hand you a piece of paper with a stamp, regnr, and amount of passengers. No one will say anything
, but you have to pay road tax at the person sitting on the left. If if it is a sedan it will be E50(equivelent to R50), if you have a van/minibus it will be E80. Then you get back in your car, stop at the boomgate, show your piece of paper and your road tax receipt. They might ask if they can see your luggage, just be friendly and patient. If you are lucky, all of this shouldn't take much longer than 30-40min. I've done it in 15min, so good luck!! Hope this helps.
PS If you have a rental car, just make sure they give you a cross border permit when you rent it!