A smaller blade will work, but one has to swing a lot harder and a lot more than with a larger blade.
Something that would take 15 or 20 chops with a 6" blade can be done with 1 or 2 with a 10" blade depending on the knife.
With shorter blades it's faster and easier to batten them through the wood than to chop with them.
I would say an 8" blade would be the min that I would consider to be a chopper, if I knew I was going to be chopping wood I wouldn't take anything short than that with me.
That said, yes the shorter blades will work (a 4" blade will work, but you would be there all day), but like I said one has to work a lot harder and longer at it.