You don't have to delete the old speech profile, as it'll still work with the old headset, however I'm not sure whether switching to a recording device also switches to a speech engine profile associated with it. You may need to do so manually.
If you use the profile for one microphone with the other hardware, recognition will likely be very poor.
To switch devices on the fly, you can set up a command for that using the "Change Audio Devices" action found under Other > Windows, so you can use both.