In my experience with felting it won't unravel. The felting melds all the fibers together and makes it a solid piece of fabric. You know how a piece of felt from the fabric store looks? Kind of like that. Have fun!
I don't have a problem with authority, I just have a problem with people telling me what to do.
As Jayme says, once you have felted an item, you should be able to cut into it like any other piece of woven fabric.
If you are using a very bulky wool or heavy weight wool, you may have to refelt it briefly once you cut out the holes for the handles. I'm not saying this will be necessary, but you may find that the raw edges in the newly cut holes will need to be 'felted'. I have felted these small flaws by hand so as not to affect the overall size of the finished project. Does this make sense???
Good luck. If you can, post a piccie when finished so we can have a peek.