A new fan, particularly if it's a quality type with ball bearings, ain't gonna cause any fires... unless it gets a cat stuck in it or something... and even then, it ought to have a ~80-120C thermal fuse in the motor winding, preventing tabby flambé.

If you STILL can't sleep, run the friggin' fan on a power strip with a fuseholder fitted with a flea-current fuse. It'll probably pop at the next power surge... but ya know.