If you wish to transfer files directly between your iPads, in absence of iCloud, consider using AirDrop:
Use AirDrop on iPad to send items to nearby Apple devices - Apple Support
If you have a large number of individual files, consider creating a ZIP-file, then simply AirDrop this compressed file to your new iPad - where it can be extracted into individual files:
Create or open ZIP files on your iPhone or iPad - Apple Support
Be aware that any music that resides within your iPad's Music Library (accessed using the Music App) cannot be transferred between devices. Music imported to the Music Library must instead be imported from the original source.