Lightroom :: Deleting JPGs Before Importing When Raw File Of Same Name Exists

I shoot raw + JPG and wish that LR 5 had an option not to import JPG when there is a same-named raw file. Lacking that, are there suggestions perhaps for Windows utilities that would do the following (I am on Win7 64-bit with LR 5.2):
 
I delete all the JPG images before proceeding. That's easy enough; in Windows Explorer, one can sort by type, then delete all the JPGs, or one could open up a command prompt in the directory and "erase *.jpg". But there's a complication; in some modes of the camera, no raw file is generated. In those cases, I just have one .jpg that I want to keep. Here is an example:
 
img1.cr2
img1.jpg
img2.cr2
img2.jpg
img3.jpg
img4.cr2
img4.jpg
 
I want to process this directory and end up with one file of each filename, as follows, before doing my import:
 
img1.cr2
img2.cr2
img3.jpg
img4.cr2
 
The pseudocode would go something like this:
 
Sort files by filename fname
 
IF fname.jpg and fname.cr2 both exist THEN delete fname.jpg
 
How can I easily do this?