Seems that I had all drives set to 'do not move to recycle bin - delete immediately' which I supposed would eliminate the nag, but it isn't so. Setting all drives delete cache to a finite size and THEN deselecting the prompt works. Thanks for prompting me about the prompt, promptly.
Setting delete to NOT put the files in the Recycle Bin EVER, can be dangerous, especially if you delete a file by mistake. It's GONE!
I leave the defaults set for the Recycle Bin and if I want to delete stuff without it going into the Bin, I just hold down the left shift key when I hit Delete..... and OUT IT GOES! Simple and much safer.