IOS – Removing camera button on iPhone lock screen

I'm including the ones mentioned in your answer in the name of having a complete listing in one place.

• Toggle music controls (Play/Pause, Previous, Next, Volume) by double tapping the home button.
• Take pictures and videos by sliding the camera button.
• Invoke accessibility features by triple clicking the home button. Configurable in Settings-> General-> Accessibility-> Triple Click Home. You can configure toggling VoiceOver, toggling White on Black, toggling Zoom, or asking which to do.
• Make phone calls by tapping the Emergency Call button and dialing a number. iPhones only.
• View snippets of emails, text messages, and other notifications by looking at their notification preview. Configurable in Settings-> Notifications-> App.

• Activate Siri to make calls, send text messages, send emails, get directions, check calendars, etc. by holding down the home button. Configurable in Settings-> General-> Passcode Lock. iPhone 4S only.

• Take a screenshot by pressing the home button and sleep/wake button at the same time.

• Power the device off by holding down the sleep/wake button.

If you are using iOS 6 (which I am, I can't get iOS 7 on an iPod 4) and the power is on, no matter what you're doing, the easiest way I found was to press the sleep button to put it on standby, press it again to turn it on, find the little camera icon that's next to the "slide to unlock" bar, drag it up to open the camera, and capture your moment.

Of course, this answer is very conditional: it only works if you have iOS 6, the device is either on or on standby, and you do not have a passcode (if you have a passcode, it makes you type it in before you can use the camera). But it works for me all the time, and I think this would work pretty well for others, too.