Yes, it is indeed a comma splice. "I'm sorry. What did you say?" Is the best way to fix it.
Now that you do understand comma splices, I can move on.
"Sorry, what did you say?" is not a comma splice because it could be qualified as an interjection or an introductory phrase.
However, it is only one word, so being an introductory phrase is a stretch.
Although they are incorrect, comma splices are generally accepted during speech. If you are speaking or writing dialogue, feel free to use commas however you want. You may also wish to consider the possibility of replacing the entire thing with just, "Sorry?" in these informal settings.
Aside from the previously stated things, I believe you are correct. The semicolon does seem to have a different connotation than the comma.
In the end, it becomes a question of "Which is more important?"
Correctness or Connotation
Remember, authors have the right to choose.