Great question, David! We already answered you via e-mail, but I'm going to post an answer here too for anyone reading the forum.
We don't plan on adding an actual option to disable the click because it should turn off when you flip the silence switch on your device. I know all iPhones have this switch, iPad doesn't, and I don't know about iPod Touch. Even if your device doesn't have the silent switch, you can still turn down the volume. (Of course, if you're listening to music while using Stop Watch, you'd have to turn down the music too, but it doesn't sound like that applies to you.

)
Again, we hadn't planned on adding an option for this, because the silence switch is a little more readily available. If you or any else would still like an option to turn off the beep despite this, just reply or e-mail us and we'll take it into consideration.
Edit: After additional e-mails, we are going to take a no-beep option into consideration, but we just released an update for Stop Watch and are now working on a new app (not to mention school is starting soon), so we probably won't be able to add this for a some time. So for now, the best thing to do is just use the silence switch or the volume buttons.
Thanks