We really cannot do anything about Team Speak causing stutters.
Keying the mic causes a lot of things to happen, in the game. There are two basic reasons a stutter will happen, related to microphone usage.
1) The game has to establish a network connection for the voice transmission. We use UDP for this, so it is as low as we can get for latency. If Windows takes time to get that connection established it could cause a stutter as that is related to handling an interrupt, which cause all CPU operations to stop, not just the game.
2) Resource usage. If Windows is getting bogged down allocating resources, then a stutter can occur in the game. NOTE: Resource allocation can be problematic, even on a system with more than enough hardware resources. It will depend on the software running in the back ground. Any anti-xxxx software can cause resource allocation issues, as an example.
There very well may be something else going on, but we have not been able to duplicate this in any system we have in house.