You could add
pushd () { command pushd "$@" > /dev/null}popd () { command popd "$@" > /dev/null}
to the top of each script. This is probably the minimum amount of work it will take to solve your problem.
In your .profile file (what ever it is called in your system) add:
pushd () { command pushd "$@" > /dev/null}popd () { command popd "$@" > /dev/null}export pushd popd
In zsh you can setopt PUSHDSILENT. Put this in your ~/.zshrc.
setopt PUSHDSILENT
~/.zshrc