I went through this before. First, I paid some deposit. Then, the seller will send the car for inspection. Once done, pay cash and immediately bring the seller to JPJ to transfer name. I did this.
Some even did online transfer while waiting at JPJ to transfer name. U will want to minimise the time frame from paying the full amount and transfering name. Anything might happen.
However, there must be some sort of trust between the seller and buyer. It is easy for either party to cheat. So, just be extra careful.
Or, u can bring the total cash to JPJ and meet the seller there. Let him count the money himself in some place safe in JPJ. Once he is satisfied, collect the money back and tell him u will give him the money once the name is transferred at the counter itself. After the transaction, you drive back your new car with the grant and he will be go home with the cash. The risk of being robbed is high, however. The buyer may be robbed on the way to JPJ from bank or house. While the seller may be robbed from JPJ to the bank or house. This is especially of the amount is big.
I remember the time when I was driving from the bank that I withdrew my money from to JPJ. Bringing more than 50k with me and I was only with my gf. Drive as fast as u can, beat traffic lights in quite roads. Scary man. hahaha.
Good luck.