Very low noise high pass filter design
Yes, we only want to eliminate 1kHz


A notch filter can be used for this: -



This is a 10 kHz design and note figure 6 - how it responds as you get between 9 kHz and 11 kHz with the input signal.

This article describes the circuit in more detail and provides examples of other notch filters across the audio range. The article is by TI and is entitled: -


  An audio circuit collection, Part 2


Regarding the op-amps, because you are using a lock-in amplifier it's not critical BUT just in case go for op-amps that are below 10 nV/\$\sqrt{Hz}\$ specified on noise. Devices that spring to mind are OP1177, AD8605, ADA4528 but there are plenty with lower noise.