...hmm, OP's magic comes from having exactly the module that you need. Applying a different module could work if the lens construction and the glasses used are the same as the one of the lens you used.
Editing exif data seems to be a bigger hassle than using manual corrections except if you change exif on a bigger batch of files using, say, exiftool. But first, you need to find the right exif section(s) to edit. Sections might differ with camera model and firmware used. Using a hex editor might be good enough or not, depending on wether you can read the data you get...
Adobe provides a toolset that you can use to create lens profile, but they only work in Lightroom and maybe some other products.