Adding caps will certainly make things worse, and a 1/4 watt resistor is way too small. The math can get a little hairy, but as a first order..
The capacitor will have an impedance based on frequency Z=1/(2*PI*frequency*cap value). Rough calculation says about 339 ohms an 1KHz, and about 34 ohms at 10K. To find out how much power you need, draw a little circuit with a 2.2 ohm resistor in series with a 34 ohm resistor, and an 8 ohm resistor across all of that (if 10KHz is the highest frequency you need to worry about having a lot of energy at). Resistor series / parallel calculations will find you the total load impedance. You power supply value will tell you the biggest peak to peak signal you can put through by accident or on purpose since you could swing close to the rails. Now Ohms law (V/R) will tell you how much current is flowing in your total load. Now work out how much current is flowing in the leg with the 2.2 ohm resistor. The I*I*R will tell you how much power will be in that resistor.
To really scare yourself, work out what happens if you disconnect the speaker while things are running.
If at this point you are thinking of being super lazy and just buying a 10W resistor and forgetting about it, you might want to look up calculating the impedance of inductors, since power resistors are usually wire wound.
Isn't analog design fun?
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