Changing config files is tricky (this wouldn't work as written for me because like many many people, I keep my emacs init in ~/.emacs.d/init.el instead of ~/.emacs). Why not do something like this?
(eval (car
(read-from-string
(format "(progn %s)"
(shell-command-to-string "/path/to/erlmacs elisp")))))
Change erlmacs to just emit the elisp when you call it with 'elisp', then add the above snippet to your emacs init (or provide this setup as a elpa package).
Pro: you won't have to remember to call `erlmacs install` again when you periodically do `asdf install erlang latest`. Con: the version of erlang that gets `(erlang-start)` called is determined by your environment / the nearest .tool-versions file when you first invoke emacs.