I am not saying that it is not impossible but the current buttons control is next, previous, voice assistant, volume up and down.
I do meetings all the time and most times I know that most calls offers you to connect a headset or earbuds and to call in but watch on pc.
I most times I stay muted and am connected through a headset. If you are connected through earbuds, you can mute your pc through the program on the pc and go off and get what you need to eat.
The trouble may come in if you are getting your food and also need to respond since you are muted at your pc.
I see one option is a lot of those calls let you visually see the conference call on the pc but you can call into the call via your phone. I think if you did that option, I believe you can mute yourself as you leave to get your food (just have to carry your phone to unmute).
I know Anker has the powerconf and I was thinking it could connect to the phone or pc and could be carried and think it had a mute as well.