Ce que j'ai obtenu après une première étape de refactoring

refactor_without_exceptions.rb

def change_password
  @user = get_and_authorize_user
  @user_input = params.require(:user)

  if (old_password_match)
    if (new_password_confirmation_match)
      @user.password = @user_input['password']
      save_user_and_display_eventual_error
    else
      error_message_and_retry 'messages.users.password_dont_match'
    end
  else
    error_message_and_retry 'messages.users.invalid_old_password'
  end
  
end

private

def get_and_authorize_user
  user = User.find(params[:id])
  authorize! :update, user
  return user
end

def error_message_and_retry(error_message)
  flash[:error] = t(error_message)
  render :password
end

def save_user_and_display_eventual_error
  user_saved_successfully = @user.save

  if user_saved_successfully
    redirect_to root_path, :notice => 'Mot de passe mis à jour'
  else
    error_message_and_retry 'activerecord.errors.models.user.attributes.password.too_short'
  end
end

def old_password_match
  @user.valid_password?(@user_input['old_password'])
end

def new_password_confirmation_match
  @user_input['password'] == @user_input['password_confirmation']
end