G'day,
Well, there are many types of grape vines, they can look slightly different inside but, you have nothing to fear about working with them, after dry they work like wood and look like wood but, they are not.
The best vine pieces to use are from the very old vines, they are bigger in diameter and have developed lots of "dead wood" which is a normal phenomenon of the vines as they grow. The older fibers die off after a certain amount of time supplying the nutrients to the vine top and new growth surrounds the dead fibers and replace the dead one so, the brown colours that you are after from a vine are all dead wood/fibers the rest is all live fibers that grow in layers.
I got a big bunch of vines a few years back from a very famous local wine producer, there story is
here
Enjoy...!
Cheers
George