How to copy "Voice Recorder" files (not "Voice Memos") to iCloud

I can't find a way to copy files from the Voice Recorder app that comes with the iPhone to the iCloud. I need to do this before I upgrade to a new phone. I have a lot of recordings that are music (format: mp3). I've tried copying one file at a time, but this is too time consuming. Many of the recordings have specific names I've assigned to them.

iCloud seems to want to copy only photos, videos, and contacts to iCloud, and I need to copy documents (from "Pages"), spreadsheets (from "Numbers"), and other apps that come with the iPhone.

Need help!