This is my very humble opinion, but most of the year my coolidor stays at around 70/70 but does jump up to 75/75 at times in the heat waves of summer from weeks to months on end. I haven't had any problems yet. Some of my sticks actually smoked better at higher rh...the Man O'War comes to mind. When I inspect my stick before smoking and find it a little too moist, which is very rare, I put it aside for a little while before smoking.

I used to be very anal about my rh and temp. It was nice having the feeling of taking care of your sticks but it can get to the point where it drives you nuts. I have been to both Cuba and DR and when I think about how hot and humid it is over there it eases my concern. After ditching the hygrometer last year I have felt some weight off my shoulders.

I would keep track of a new cabinet or humi just to be sure, but if you have beads in there, I would be pretty confident everything will be just fine.