Unless there's a voltage regulator in the base of the charger, I would REALLY advise against using any power supply with a higher voltage rating.
Chargers for Ni-cad are usually what's know as 'Constant Current' which means they try to 'push' the specified Amp rating through the cells at all times. The way they detect a 'finished charging' situation is to measure the voltage needed to do so.
The fact that the original charger is listed at 19V indicates that it was supposed to pass that voltage and current directly to the battery without a regulator or anything in the 'charger' itself. All the 'smart' bits were in the power supply.
Power supplies with a higher voltage rating may be built for a more advanced charger that has the regulator built-in(the regulator causes a voltage drop down to the correct voltage)
The only reason this has worked for so long as it has is the relatively low current the replacement power supply has been able to deliver. (Ni-Cads can take some abuse like over-voltage without exploding orotherwise failing. They can also take some heat. Some Lithium-based cells will fail at temperatures as low as 50degrees C, though... )
The reason that it took 8Hours to recharge with the old charger is that he was using a 300mA power supply instead of the 2.2A model it originally came with.
I'm betting that the battery is rated 18V/2AH?
(8Hours x .3A = 2.4AH, subtract the loss and you end up close to 2AH. Same with the 19V/2.2A original PSU.)
If the new chargerworks, you'd be looking at a 12Hour recharge...