My vote: Leave it outside the humi. The leather, or faux leather, won't really hold any moisture. My case has a paper-thin cedar lining, which again, won't really hold any moisture.

A cigar case is fine to take out for the day. I think some folks would even say two days. After that, depending on where you are (Arizona's dryness vs. Florida's humidity), and depending on the RH of your humi, I would be conscious of the need for humidification at some point.