Those are typically condensers. That's why they don't have to be right up by your mouth. You said that you don't want the mic to be sensitive because that would mean it would easily pick up ambient noises, such as typing, your computer's humming/whirring noise and any other noises around you.
If the mic can be effectively used without needing to be right up to your mouth, then you're not going to like it because it will be too sensitive; it will be too good at picking up ambient noises.
I watched a streamer using lavalier mic. He is one of the top streamer at Twitch although he is using lavalier mic. Here's the link: https://www.twitch.tv/asiagodtonegg3be0