Whether you can replace the cathode resistor with a current source, and the kind of current source you can use depends on what the bias voltage across the cathode resistor is.
There is always a voltage drop needed across any CCS, and different kinds of current sources need different amounts of voltage across them. A CCS can always have more voltage across it than it needs but never less voltage than it needs. You need to choose a CCS that needs less voltage across it than the bias voltage that you want.
So, go to your plate curves for the tube that you are using. First you determine what current you want and draw a horizontal line across the curves at that current. Second you decide what bias voltage you want. Then the intersection of the horizontal constant current line with the desired bias curve will tell you what the plate to cathode voltage must be at that current to give the desired bias. So, you can choose any two of the three parameters – current, bias, plate to cathode voltage – and the third parameter will automatically be set.
The K&K CCS kit needs at least 4 volts and maybe as much as 8 volts depending upon the characteristics of the MOSFETs. You have to try them to see what they are.
If there is not much current and maybe about 2 volts of bias you could use a jfet current source.
So, generally, for a CCS in the tail of a differential circuit, for power output stages you could use the K&K CCS, and for drivers you could use a jfet CCS.
For putting a CCS in the plate circuit, the same rule holds – you can pick any two parameters and the third parameter will be automatically set. Of course, the bias is developed across the cathode resistor and you use E=IR to determine its value.
Dave