So this is only a problem for my locally saved savegame and wouldn't be a problem for others?
Maybe.
It depends what is in your Saved Game (saved games store lots of things that you would not necessarily think were stored) and what is in your mod.
What you have found is something that many of us have found. Sometimes you change something which seems perfectly fine, but - often the point at which you saved a game in skyrim - has conflicting data in it.
It's very difficult to tell you what the "thing" might be, as there are many things it could be.
For example:
Say you saved a game where your character had a particular perk and it was active when you saved
Then you mod changes to that perk (or delete it, or whatever)
When you reload the game, the perk is in the saved game, but you may have altered how the perk is used (removed the perk completely, for example)
That MIGHT cause a dirty save ... which may cause a CTD, or break game functionality ... or other weirdness.
But, from the test you did, you know that your mod has issues with some saved games. If you have other saves, try them and see what happens. It is very possible that the conflict is very specific to your save ... and possible that it is not
(Continually ... loading a saved game, playing - saving - modding - loading the newer save, playing, saving - modding ... is more likely to cause you issues than using a
clean save - and never resaving - every time).
the "new" one you get from using coc right from the mainmenu as well
I keep forgetting that exists!