Although I don't have any specific op amp recommendations, I'd suggest parametrizing the problem to aid selection.
With a maximum peak swing of 4.5V the minimum slew rate for an undistorted 20kHz sinusoid is 0.56V/us. So, even doubled for a bit of margin this isn't a particularly difficult constraint, although the amp specified should have a spec on SR at the operating voltage as it will typically get worse at lower voltages.
The noise resistance of the input stage should be a reasonable match to the transformed source Z, so e sub n over i sub n should be about 15-20k for a given bipolar input. For a FET input the i sub n component will be negligible at these impedances so look at the voltage noise in a 15k R: 15.8nV/root Hz. Thus a garden variety BiFET will give about a 3dB noise figure.
As far as gain bandwidth needs, the hidden variable here is the open-loop distortion of the candidate amp, typically worst at the highest frequency of interest. Except for crossover distortion, which high feedback doesn't help that much anyway, the stage that will be important is where the big swings are, namely the second gain block if a dual op amp is used. In any event, if we know the open-loop distortion and gain at 20kHz and close to full output swing we can fairly well determine what the 20dB closed-loop distortion will be. It also would be good to know the relative amounts at different harmonics---a whole lot of higher order might be a good reason for rejection even if the numbers for total looked good on paper.
At low powers the crossover distortion in the output stages is probably the biggest cause for alarm, and it is not well-quantified, other than to note that some low power amps are absolutely terrible unless run in forced class-A. For example the LM358 from most vendors is awful, although it cleans up a bit in class A.