Headset with “the perfect” mic, no software.

Wife works from home, unfortunately we lost the nanny we trusted the most. Until we figure this out,

wife needs a headset that would blockout baby crying as best as possible, noise cancellation both on the earpiece and microphone, so customers can’t hear babies and so wife wont get distracted when doing math stuff while on the phone, it would be best if wireless and most importantly, her company does not allow any software to be installed, so yeah, softwareless??

It is super important so im willing to spend 300 to 400……any ideas?