Lol the SATs will never be the end all be all. If you think about it, watching the time actually makes you paranoid and thus waste precious time. The best way to finish a section on time is to always feel like you're running out of time and tear through questions. I don't
mean to skim questions but rather to mark questions that stump you for more than a minute or so and move on to the next, returning in any spare time you have left. If you absolutely must have a watch though, I think taking the speaker out of a watch is perfectly fine enough. As long as you don't smash anything with a hammer the watch should be a normal time-keeping tool without any problems.