The sim card has no relation to your iPhone's data, or transferring content. All the sim card has is your number and carrier settings.
Transferring the sim card from one phone to another has no effect on your apps data or files.
If you are letting Documents store your files in iCloud, then they should come back when you log in to iCloud on the new iPhone.
Otherwise restoring a backup taken from the old phone onto the new iPhone, should transfer all the files inside the apps that are not being synced to iCloud. See here: Transfer content from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support