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.