Is there any way I can determine if the query is truly safe? My current IsQuerySafe(string) method

That rather sounds like The Halting Problem...., but

Essentially, I want to only allow select queries

Use a different database login (ie. connection string) that has only read access. Any attempt to perform a modification will be an access violation. (On SQL Serve a user with just db_datareader role would do it on the relevant database, and no access at all to others.)