How can I remove files that do not contain the number 1 or ~1?

I had to convert many .avi files.  The new names all contain ~1.  Those files I want to keep and remove the originals.  There are scripts to remove files with a numeral such as 1.  I need one to remove all files without the 1 or ~1.  I tried using a script that removed older files, but the new files seemed to have the same created dates and modified dates so that will just delete all the files.