I had the same concern.
I used a very small drill bit and pushed it into the drill as far as it would go.
Then I took a piece of masking tape and wrapped it around the bit so that only about 1/4" of bit was exposed.
Drill until the tape touches the wall.
Now you have a nice little hole without piercing anything in the wall.
I went to the hardware store and got some shorter screws.
By the time it goes through the holder and into the wall there is hardly anything sticking through into the wall cavity.
It has been that way for 4 years and been fine.
I wouldn't want to put my weight on it or anything, but it seems to be doing fine.
You can put a small amount of wood glue on the threads when you screw them in if you want some extra holding power but you should be fine.
Bill