Mute current call that came in as an incoming call but not mute for warm transfer

Mute current call that came in as an incoming call but not mute for warm transfer. A call comes in, we talk and it's determined that they need to be transferred. I mute that call so that in case they have new information to add like "I was able to get it to work now, I don't need a tech", I can hear them but they don't have to hear me typing and trying to find someone to help them. Then when I call the tech for the warm transfer, I should be automatically unmuted with this new connection instead of having to manually unmute, which adds more wait time to the initial caller.