Lots of choices-I think silk knit can work,depends on your outfit as a whole.
Also this time of year linen/cotton blends are lighter and dare I say can be less formal depending on colour or pattern.
What type of non-formal appointment is it,will you be wearing a suit or sport jacket odd trouser combination?
Seriously, without additional details, it's impossible to provide a meaningful answer. It's like telling us that you're going to a non-formal restaurant, and asking what food you should order.
I m sorry but I don t know what to do if you don t understand what i m trying to tell. I m only looking for a tie that i can dress without have a too classical style but as much as possible casual... and never mind if your answers are too generic