Wrye bash does this for all games it works with: Morrowind, Oblivion, Fallouts, Skyrim.
Just look at the saves tab and they are all listed in a side panel.
But that alone will not tell if a mod is baked into a save. Any active esp will be seen as a master for a save - that is unavoidable. Any clean save and they won't show again on the next save.
The baking into a save that is dangerous is mostly about scripts being baked in - that can be seen by enabling papyrus logging and then playing with the mod active - remove it - run the game again and see what is throwing errors.
[edit] there are other things one can edit I think that can be a danger to move, but what has caused most of the hullabaloo over the last year is the papyrus scripts being baked in and no assured way to clean them out once in.
[edit for clarity]