You can eliminate capacitors in the signal chain no problem, but you can't eliminate them in the power supply section. You could use super capacitors that act like a battery, or even a battery... But even batteries sound different.
Frankly if you want music as we know it, you can't not have capacitors in the power supply fashion; again you can only eliminate them from signal.
The capacitors in the power supply never carry "signal", they provide raw DC power that turns into signal before it leaves to the speakers. The frequency of DC is essentially 0.
The FirstWatt amp series doesn't use signal caps in several designs I believe. You can still roll resistors, or just fork over $12 a pop for nude Vishays knowing maybe an LDR would be better but not enough to care.
You could remove signal caps in any amp if your source provided no DC on the output.