How will the resistance of this Evaluation Module affect the measurements of the current produced by this photodiode?
If that's the case, then I can put some resistance I know, like 1
  kOhm, in one of the terminals of the photodiode, connect that to the
  Evaluation Module, then connect the other terminal to ground, and
  that's it.


Why put a series resistor in at all? The 1128 converts current to voltage internally, and the electron source in your photodiode is modelled as a current source - so don't bother. Just connect the lower pin in your PD schematic to ground, and the other to the 1128 input. Easy, peasy, pudding and pie.