Or "SCRAMBLE"

But, I'm confused on the rules. You said "add or delete one letter", but in your example, "skim", the two given, "milk" and "mile" do not have added OR deleted letters, only changed letters! So, are the choices to add, delete or change one letter, and rearrange if desired? Here are mine:

BRAN (shea.. he he)
BAIRN (love that word!)
ROBIN
BARING

And continuing from Alex Williams's:

LASING