I think you mean wider, where I was thinking the problem was making the stick longer at the end.
You can use brass nails and hammer them down like rivets. Easy way is to just use the nail and hammer the pointy tip down, then wrap in tape so you dont get snagged by the bent nail. Will only add a milimeter in thickness. I use this for corded nunchaku a lot. If you have very thick dowels to start, you can even make a wooden pin which is easier to work with and which you can sand down so it is flush with the baton.
Fancier way would be to drill a hole first as close to the exact width of the nail. Then heat up the nail until it is glowing red and quench it immediately in water. This will "anneal" the metal, making it softer to work. Put the nail through the hole and cut off both the head and the sharp bit. Lay this on a flat piece of metal (an anvil if you have one
)
Hammer both sides down, hitting each side once and turning over to keep both sides exactly the same. First couple hits will be the most difficult, because you don't want the rivet to bend, you want it to flatten out like a pancake. Eventually, you will have a rivet. This will be prettier, but no more functional than a bent nail.
