Here is another idea. Dictate your text messages. I found that the Google voice (see microphone symbol in lower left corner of keyboard) works with 97-98% accuracy. For that reason I now dictate text messages and EMAILs sentence by sentence. It even handles it when I say period at the end of a sentence. I then type two spaces and dictate the next sentence. It works for me.
By the way, if it makes an error I can go back to the error and fix it faster than I can type the text message itself and who says that my own typing is error free!!!
I now use text messaging much more because of being able to dictate the message.
You probably know this but you can quickly silence your phone while typing a text message by pressing the lower volume control button (left side of phone) until it's at zero volume. After you're done typing the text message press the upper volume control to return the sound to the phone.
This totally silences your phone but it is quick and you do not have to leave the text messaging keyboard page to use it.
It is probably as close as you'll ever get to achieving your goal.
By the way, mine gives a very quiet single click when I press a key. It's not a tone and it's barely audible.