"I want advice on how to replace the rear wheels of my Toyota Camry with snowcat treads for better handling in winter weather."
"That doesn't seem like a good idea."
"The negative comments can be kept silent."
Don't know why I'm taking the time for this, but...
A Steam cache is when you download all of your game files to your local server so that when you want to install the games on to one of the other PC's on your local network you just copy them over from the server. The advantage of this is only have to download the games once, so it's nice for people with slow internet.
It sounds like you want to forego installing the games on your labtops laptops at all and think you can stream the files across the network when you want to play. That... is probably not practical.
FWIW I have fairly successfully run steam games off of an iSCSI share before with few to no problems, this doesn't work great if you want multiple hosts accessing the game files but as a way to add storage to a computer it can work *fine*.
If you give even a little bit of reasoning as to why you think something won't work it becomes infinitely more valuable and will be perceived as far less negative.