Hi, my son is 9 months also and he really struggled with finger foods at first from about 8 months...he would get the food in fine but he just didn't know what to do with it when in his mouth..
What I started to do was give the finger food as small as possible to get him used to being inderpendant and still enjoying the food... but the pieces small enough that he could develop the chewing motion and the way to prevent him gagging.
Maybe try at first some TINY pieces of cheesestick or bread with vegie then start giving the pieces a little bigger when you feel he is more confident at eating them. And make sure that the food is more softer texture so it is easier at first.
My son now eats sandwiches, rice cakes, vegie chunks, chicken breasts small pieces, pasta...pretty much whatever we have though smaller...
He will get use to finger foods over time...it took 1 month for us.
Mum to Jai and Chase!