Having offered advice, I'm having difficulty in answering this one...
It all depends upon the weather! Currently the forecast for the whole weekend is looking very good. I will post a weather update sometime next week.
Some runners have supporters waiting between Wengen and Wixi armed with warmer clothing but generally this is not necessary and most people seem to complete the course wearing just a vest.
I asked a friend who has done the course several times and he said that apart from one year when it was very wet he has never needed additional clothing. He suggested that sunburn was sometimes a greater problem!
Personally I'm planning to hedge my bets by wearing a t-shirt style top rather than a vest.
I'm sorry that I can't give you a definitive answer.
Steve