405winchester, The diameter of your cannon's muzzle depends on two other factors. These are the amount of taper from breech to muzzle and the length of your tube. We really hate to assume anything, but we will assume two other things here to make it easy for you to make an elegant, good looking tube, rather than something that looks like a circus tent stake. We will assume that you will buy enough steel of 4.5" Dia. to make a tube of 24" or 36" length and a bore size of 1.5" Dia.; why cause yourself unnecessary grief with forming a chamber? If the owner ever wants to shoot this thing, the sponges and worms and powder charges are much, much easier to build with a straight bore and chamber, besides, golf balls are extremely poor projectiles, with 1.5" lead or zinc balls being at least a hundred times more accurate!
So then, what's a good looking taper? The Dahlgren boat howitzers look really nice with tapers of .44" dia. per foot of length. Most of the good looking field gun tubes of 6 and 12 pounder size, use a similar taper and the CW howitzers, both Union and Confederate used a .60" dia. taper per foot. The 24 Pdr. Flank Howitzer, M1844 is one example. For a relatively short cannon, as your's will probably be, it is decent looking. Without a taper it would look like a section of sewer pipe laying beside the road next to the ditch.
If you make the tube 24" long, with a 4.5" Dia. at the breech and a taper of .60" Dia. per foot, the muzzle diameter will be 3.30" and the wall thickness at the muzzle will be 1.15".
If you make the tube 36" long, with a 4.5" Dia. at the breech and a taper of .60" Dia. per foot, the muzzle diameter will be 2.70" and the wall thickness at the muzzle will be .60".
Either of these would be pleasing to the eye, and especially if this gun is to be a gift, you want it to look that way.
Mike and Tracy