You can skip the bypass caps in a battery-supplied circuit. They are there to shunt any AC to ground, but you won't run into much of that.
What's your goal in doing this though? You may be throwing away runtime because the regulator dissipates quite a bit of energy to do its gig.
Did you measure the Makita battery under any kind of load? (I know the answer) It would be a good idea to figure out what kind of load your device presents, and pick a dummy resistor to simulate it, then measure the voltage at your battery. You may not need to do a damn thing to your battery.
Dummy load example: say your dingus draws 50mA current. The resistance that would give you that load current with an ideal 9V supply is R = V/I = 9V/0.050A = 180 ohms. The power dissipated in the load is going to be 9V*0.050A = 0.45W or 450 mW. So you'd want a 1/2 watt resistor for your dummy load (preferably a 1 watt).
The load current you (likely) measured under was effectively zero into a infinity ohm load, so the battery isn't behaving the same way as it will under load. The batteries have a series resistance of their own that will cause the voltage seen at the terminals to sag under load (more under larger loads). The way you (likely) measured won't account for that effect.