You probably don't want a wirewound resistor in a feedback loop as they can be inductive. That's a potential oscillator. Also, the current in a typical opamp feedback loop should be very small, so I don't think there is a big concern with noise.
Whatever thermal noise you get from the series resistor will be shunted along with the signal, so the noise addition will be small. Note that amplifier circuits tend to have lower equivalent input noise at higher gain, partially for that reason.