In my experience. the inner cable will push through a hole in the hand-grip side or the edge facing the ground. There will be a black or grey plastic grub screw that will use a screwdriver, torx or hex key to remove. It won't be tight. The hole will be large enough for the round end of the bowden cable to fit through.
Again, if you have this hole then you do not need to remove the top plate.
Not a great picture but similar concept, opening an access hole to push the inner through:

Since you're changing the inner, its prudent too change the outer too.