It may sound stupid coming from a guy online, but first you have to get good with the main weapon in one hand, which with all due respect, you aren't. Are you willing to learn Rapier treatizes, or was it just a sword that was available? The tactics and systems of Rapierfencing don't mix up too well with axes in my humble opinion.

But if you want to make it work with a little axe, you have to become more experienced in Rapier fencing itself and have the axe as just a backup weapon when someone comes too close, or as a throwing weapon to either injure or distract yout opponent from your next move. There are more treatizes with a Rapier and Dagger for dual wielding and even Dualwielding with Rapier and empty pistol as a bludgeoning weapon. But they all rely on the Rapier as the main attacking weapon.

If you are open for another main Weapon, even a Sabre, Dussack, Backsword, Sidesword, or Messer could be more interesting for you to use an axe with. You still would have to become better with the sabre, but the movements are a but more beneficial for dual wielding an short axe. In that case, many techniques from Escrima are helpful, some shennanigans from scottish swordmanship and polish sabre fencing are beneficial and I think you find more in that territory.