I have System Preferences set to announce the time every 15 minutes, and some filters in Mail.app set to let me know when a client's e-mail arrives.

I always forget to turn them off when I want to record something. I actually I only remember I should have done it when I get a timecheck or a beep in the middle of the recording, and it can be quite misleading if I hear it during playback.

Is there any way to have WireTap turn these unrelated sounds off automatically when it begins recording, then turn them back on again when the recording is stopped?

There isn't a way to turn these sounds off automatically.

However, you'll be happy to know that with WireTap Pro 2.0 (currently in development) this problem will be resolved entirely. So, keep an eye out for 2.0.

For those of you wondering, I can't give you an ETA for WTP 2.0, so please don't ask.