Would it be safe to plummet the humidity in my house to around 15-20% to drive out insects?

Not it is not safe. When humidity in your home is too high or too low, it can make living conditions unpleasant, and it can also do lasting damage to the property. The level should be from 30% to 50%. At lower humidity levels, the effects can include dry or itchy eyes, dry skin, and infections spreading more rapidly. Dry, low-humidity air also causes physical damage to the home. Wood contains a certain amount of water, in ideal conditions, and when it loses too much moisture in dry air it experiences shrinkage. This can result in serious damage to flooring and furniture, or shifting window panes. Low humidity can also generate excess static electricity, which sometimes affects electrical equipment and computers. You need to find another way to remove insects.