It is not that easy. I am assuming that you wish to retain the existing 2 cables and then you have to squeeze the 2 into the 13 pin socket. Yes, it can be done but it will be a lot of fun and probably lead to alot of interesting language, especially f you are lying undre the back of the tow car at the time. You will then find the grey socket you currently have has thicker wires than would be the case of you use 13 pin cable, so care needs to be taken. If possible replace the cable with proper 13 pin cable and then do the 13 pin socket. This means reconnecting the cable inside the tow vehicle.
It may be better to chicken out, hit the ATM and get a tow bar specialist to rewire it for you.
However, having used the adapters, first one way, and then the other due to changes in both car and van, I can state that touch wood I have never had any problem. Just keep the connecting pins clean and dry