Docking is not so reliable approach to get the proper conformation and binding of ligand. It may provide a preliminary idea. To get the proper conformation you should do the molecular dynamics calculation and analysis.

Agreed. Even with the same system you will get different docking results depending on the software and limitations/restrictions you put on the system. A short 200 ns MD simulation will be more illuminating if you want an idea of what difference the cofactor makes energetically.

MD simulations should give you an approximate answer to your query, you may also apply related force fields to get closer.

The important aspect worth to look at whether the cofactor develops any interaction with your ligand. If no, then there is a high possibility to generate similar results assuming the reproducibility efficiency of the program is high. A quick and rough conclusion can be drawn why the docking programs produces similar results with and without cofactor by doing these simple tasks. Cluster your ligands based on Tanimoto coefficient and consider docking the representative ligand with and without cofactor in multiple protein structures of your target. Calculating an average and standard deviation will provide you some clues: what may be the expected docking energy for a particular ligand in both presence/absence cofactor sets, averaged difference between cofactor and no-cofactor profiles, etc. If the averaged difference is too low (e.g. -2.37 kcal/mol for AutoDock Vina), you may come to a conclusion that the cofactor contributes very least to the docking energy. You may also do this task with single target structures by changing the Force Fields, Sampling Methods and Convergence Criterion. I am giving this guidance assuming the unavailability of resources to perform long MD. Another aspect to examine whether your docking program takes into account metal-het atoms/protein atoms pair potentials (assuming cofactor is a metal; e.g. Zn2+, Mg2+).