Is there a genre that could be called "Safe Thriller"? It seems that all thriller novels are R rated. A PG rated thriller could still be engaging and serious without gross content. Similar to a "Cozy Mystery"?
This is the sort of question you can best answer with a stroll down to your local bookstore. But consider: thrills come from danger. You need to be strapped in to ride the roller coaster. A book let's you take a thrill ride with the safety harness off. The roller coaster is probably the preferred source of safe thrills.
Goosebumps would probably be your closest bet to what you are looking for. It is children/teen series that does a PG horror/thriller story. I use to read them a ton growing up and I hate horror or thrillers for that matter.