As far as I know it is not possible to manipulate the stored exif data in a photo. To do that, you could try “exiftool”.
But within the export module you can store a preset for each manual lens and use it on export. You only have to switch between the corresponding presets.
Maybe not an elegant way, but this is the way I use it.
The data in the lens correction module is not used to manipulate the exif data, but to correct distortion or chromatic aberration.
I don’t think you can “read” this out. Maybe with a LUA script… but I don’t know about that.