Is there any way to move document library from sp2013 on premises to sharepoint online without use of azure blob storage. Reference - https://blogs.technet.microsoft.com/nishants/2015/07/18/using-windows-powershell-cmdlets-for-sharepoint-online-o365spo-migration/
Yes, you can move document library from sp2013 on premises to SharePoint Online (O365) without the use of Azure blob storage either by writing your own code using the SharePoint REST / CSOM API (or) by using any third party SharePoint migration tool such as Vyapin's Dockit Migrator for SharePoint.
If you have any complex datatype columns in your document library (such as taxonomy, look-up columns etc.) or if you would like to retain SharePoint default column values (such as 'Created by', 'Created', ‘Modified’ etc...), then my opinion is you can opt for third-party SharePoint migration tools.