Short bursts of high humidity shouldn't pose a problem, and can even be beneficial, especially during the shedding cycle.
However, long-term periods of high humidity can cause health problems such as fungal infections, scale rot and even the onset of a respiratory infection.
You should be aiming for 40 - 50% relative humidity on a consistent basis, but you should raise it when he's in shed (by creating moist hides using sphagnum moss, misting etc.)
If you want to reduce humidity, you can melt/drill some more holes in the tub to increase ventilation, you can make sure that the water bowl is in the coolest part of the tank, and you can use substrates that don't hold humidity very well (e.g. paper towels, newspaper etc.)
All the best
David