That won't work. If you select the spell, you'll just have it in both hand. He's talking about RIGHT hand, not left hand. The only way to unequip the right hand spell is to do what I said above.
On the contrary, I just did this. I've done it with the spell in both hands and I've done it with the spell in the right hand and a shield in the left. Go to the favorites menu, and select the spell again.
It works just like a weapon. Select it again and it's removed from your hand.
Now, key point: what platform are you playing on, and if PC, what control device? Because that might be the key.