Dash rc files for non-login non-interactive shells

Question

Does dash have a non-interactive non-login rc file? I've read the man page, which recommends .profile for login shells and $ENV environment variable for interactive shells.

Is there anything that runs for non-interactive non-login shells, such as zsh's zshenv files, or bash's $BASH_ENV environment variable? Is there an equivalent file for Bourne shell too?

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Best I can come up with so far (although not ideal at all as it requires me editing every single script) is to edit the shebang as follows:

#!/bin/sh /path/to/script

f

where /path/to/script contains

f() { echo "/path/to/script"; }