You don‘t need a special tool to verify. In the skype download there is a JSON file with all messages. Do you know JSON?
I will PM you for the exchange of the file.
You can see the skype id in vareole‘s post.
https://archive.vn/FtBwsThe main problem is with the fact that text files et al can be edited easily, after the fact.
If you can imagine a way for you to fake the details, then you can understand why it's difficult to verify the evidence without having direct access to anything.