How to launch .sh scripts from the finder in iTerm2 instead of Terminal

This is a little bit hacky, but you can achieve this in AppleScript. If there is a predetermined number of tabs you want, and preset commands you wish to run, this isn't difficult.

tell application "Terminal"
    -- Activate it.
    activate

    set targetWindow to 0

    -- Get a window that's not busy.
    -- If there are no open windows, open one.
    if count of windows is greater than 0 then
        repeat with currentWindow in windows
            if currentWindow is not busy then
                set targetWindow to currentWindow
            end if
        end repeat
    else
        do script ""
        set targetWindow to window 1
    end if

    -- Do command 1.
    set firstCommand to "cd ~/Desktop; clear"
    do script firstCommand in targetWindow

    -- Open a new tab.
    tell application "System Events" to tell process "Terminal" to keystroke "t" using command down

    if count of windows is greater than 0 then
        repeat with currentWindow in windows
            if currentWindow is not busy then
                set targetWindow to currentWindow
            end if
        end repeat
    else
        do script ""
        set targetWindow to window 1
    end if

    -- Do command 2.
    set secondCommand to "cd /Applications; clear"
    do script secondCommand in targetWindow

    -- And so on...
end tell

Of course, replace firstCommand with whichever command you actually want to run, and so on. For whatever reason, Terminal doesn't really have an accessible way to create new tabs through AppleScript, so the long, hacky looking line in the middle just tells Terminal to type ⌘T to open that new tab, and then new commands will execute in it.

You can run this AppleScript as is, or use it in Automator to create a new service, which you can then execute from anywhere using a keyboard shortcut if you'd like.

Extras - If you want to fire some script/command in the newly opened terminal session, you can refer this

The exact sorting order used by Finder probably depends on the locale, but scripting languages like Ruby and Python have libraries for sorting strings naturally.

#!/usr/bin/env ruby -rubygems -KU

require 'natural_sort' # gem install naturalsort

input = "name-II-1
name-6
name-2
name-19".lines
# input = Dir["#{ENV['HOME']}/Documents/*"]

puts NaturalSort.naturalsort(input)