Transfer SMS message history, without Google account
There are several apps supporting to Backup SMS/MMS (and of course also to restore them), running locally in &quot;user-mode&quot; (if you prefer cloud storage, which by the question you do not, there are also ways to Backup SMS into the Cloud).
As your devices have root support, you might consider using Titanium Backup – which allows you a.o. to export your SMS/MMS as XML files (and also to restore that, of course). This solution should definitely work with CyanogenMod (while above mentioned apps should as well).
A note on the &quot;backups via ADB&quot; RossC referred to in his comment on your question:

Can adb be used to recover SMS messages while in permanent “Safe Mode”? deals with backing up the corresponding database file. When chosing that approach, you should make sure to only restore that on the very same device, ROM and Android version (e.g. after a factory-reset, but never after a ROM/Android upgrade or on a different device). Otherwise you might run into trouble (says one who had that issue in the past, so you can believe it ;))
How do I backup data (SMS/contacts) from a device with a broken screen? has answers with the same approach (to which the same warning applies), but some answers also mention tools simply utilizing ADB to access the device. I've never used any of those (as most seem to be Windows-only – like Moborobo, Myphone Explorer (most famous solution for Windows-people, offering a lot more than just SMS), Mobogenie, DroidExplorer (the dev is active here!) – and I'm on Linux – my only windows are for light and fresh air), but I'd assume they do more than simply &quot;copy the database file&quot;, so they might fit your requirements. Still, for above reasons, read their instructions carefully.