Here are a few methods you can look into:
- You can refer to this post for a workaround to export version histories from an XML fie: sharepoint list version history export to excel.
- Here is an Open Source Project solution called ExportVersionHistorySP2013, which needs to be deployed in your farm before you can use it.
- I would still recommend using PowerShell since it is the easiest way. Here is a sample script in case you change your mind: Export SharePoint List Item Version History to Excel using PowerShell.