How to make a hat insert for military cap?

My husband would like me to knit him an insert for his wheel cap. Think Marines…It would need to be round and his hat size is around 7 3/8 inches…I was thinking I could knit in the round on circs like I would start a hat…then just start decreasing right away so it essentially would turn out to be a flat hat…I thought this would be easier than trying to knit a perfectly round dishcloth with straight needles.

Does anyone have any thoughts about this? I am a complete rookie, so I have no idea how to figure this out. Maybe someone has a pattern for this type of thing? or suggestions of how many stitches, and how to do the decrease? Any help or advice would be appreciated. This is the only thing that he wants.

I won’t pretend to know what a wheel cap is. I know it isn’t a helmet, but you might find some usefuly links at this site to get you where you need to go to find a pattern?

It would essentially be a perfectly round dishcloth…to fit inside a hat like police officers wear