Hey,
This is a good question about 3 different conjunctions which are easy to confuse. Before I answer your question, I just wanted to note that these conjunctions differ in frequency. “While” is quite common, “whereas” less common and “conversely” is rare and formal.
In the example sentence, I agree with the last comment that none of these words fit that context.
Generally, you can use “while” and “whereas” interchangeably as long as you are talking about a contrast (because “while” also has a different meaning).
For example:
Japan is an island whereas Russia is not.
Japan is an island while Russia is not.
The conjunction “conversely” is used to suggest a contrast not just in a simple fact but in someone’s opinion/outlook. As such you will see it in academic writing/essays/newspapers etc