It will work without a SIM card.
A backup to iCloud will transfer all of your settings to the iPad Air, when you restore from it. Here's what else is backed up by iCloud:
What does iCloud back up?
Depending on what else you need to transfer:
Photos will be synced to the iPad through iCloud Photo Library.
If you have files that don't sync to other iDevices, save them to iCloud Drive (an app made available by Apple), so they will also be available on your iPad Air.
Online services such as Dropbox, OneDrive or Google Drive will show their content on any device as soon as you log in.