What kit are you talking about that you need that's only comes in 1/4? I'm really a visual girl, so can you point to some links that show what you're talking about. I had water change systems running all over my house. We can definitely make this easier for you.
https://www.thespruce.com/saddle-valve-2718691
I could not find this kit in 3/16th. 1/4th seems to be the smallest.