I have the free version of EndNote Web and use the Cite while your write Plug-in.
I am submitting a textbook chapter that requires Vancouver bracket style. Can I edit the already existing Vancouver style to brackets  instead of paraentheses ()? I have tried and nothing seems to work on the Plug-in or online version.
I don’t know if there is another style that would have the square brackets, and modifications which would automate the process are not possible with the free version. You might try formating a copy with IEE (which is square) and then another copy with Vancouver, and stripping the fields of the first and copying the bibliography from the second into the first?
Always keep an original endnoted version of the paper in a safe place, for the inevitable modifications/revisions later.
Stripping the fields, is most easily done with the “convert to plain text” option on the endnote ribbon.