vim with servername as default editor in zsh

I'd like 'edit' in zsh to start vim with v:servername = VIM.
Here's what I tried but to no avail, perhaps someone knows how to do better?!

In .zshenv there's a line

export PATH="$HOME/bin:$PATH"

and in .zshrc there's

export VISUAL=vim
export EDITOR=$VISUAL

and in ~/bin there's an executable file 'vim' containing

#!/bin/sh
vim=$(which 2>/dev/null -a vim | tail -n 1)
exec $vim --servername vim "$@"

Then $EDITOR and $echo $VISUAL show 'vim', but 'edit' and ':echo v:servername' is void (in contrast to 'vim' and ':echo v:servername' that shows 'VIM').

Best wishes

Enno

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