Your question isn't really specific to LabVIEW, as the same exact question can be asked for any programming language. Which speaker are you referring to? Are you talking about a speaker that's built into the computer that might beep when you turn on the computer? Are you referring to external speakers? If you're referring to the built-in speaker, I know of no way to turn that off from the operating system. You could record a silent sound, save it as a .wav file and associate it with the sounds that make the beep. Or, you could always yank it out.
