It sounds like you are planning a J style rocket.
If so,6" is the smallest size recommended.
Smaller J style rockets tend to be finicky.
Don't worry about it being too big, the thermal mass dampens the extremes of the heat.
In some ways, the rocket is like a
bucket used to fill a bathtub(the thermal mass).
The bigger the bucket, the faster you can fill it...
I would consider putting
cob all the way up the sides of your barrel,leaving only the top bare.