You might be able to use the NiCd charger to put charging current into the battery. It's the part where you "wait until finished" that the problem arises. The charge termination schemes (when to automatically stop charging) will be different. For lead-acid, probably switching from current-limit mode to voltage-limit mode at some maximum safe charging voltage. For NiCd/NiMH, watching the voltage for where it goes "over the hill" from increasing to decreasing, and/or the temperature rises quickly. Plus some other safety features, such as timeout, over/under-voltage, over/under-temperature, etc.
If you put the wrong chemistry on the charger it may never see what it's looking for to cease charging, because the battery behaves differently (voltage graphed over time has a different pattern). It could keep charging literally until the battery explodes. If you understand what the battery requires, and what the charger does, you might be able to use it anyway, to the extent you can manually observe and terminate charging as appropriate. You're risking destroying the battery, but in some cases getting a partial charge right now is more valuable than a longer lifespan later.
Your stated goal is measuring the capacity of the battery, rather than, say, getting enough charge back into your car battery so you can start the car and drive it around to finish recharging. If all you wanted to do was get "some" charge into the battery, considering you already know it's discharged, you could probably let it charge from your 2A source for "a while" and disconnect it manually after some time considerably less than (64A-hr/2A)=32hr, say 8-12 hours, watching with a voltmeter that the voltage doesn't exceed the maximum safe voltage and disconnecting early if it does. For your purposes of getting the battery fully charged and discharging to measure capacity, you'd want a proper charge termination scheme, which you don't have.