You will likely adjust to the stinging over time.
You can allow the magnesium oil absorb into the skin, and then wipe the area with a damp washcloth.
Or you can dilute the magnesium oil with water, or make a lotion. I enjoy a homemade lotion using equal parts magnesium oil, coconut oil, and aloe vera gel. You can try a 50-50 mix of magnesium oil and almond oil, or whatever works best for you.
Magnesium expert Dr. Mark Sircus finds the itching is caused partly by impurities and contaminants in the oil. He recommends using ancient minerals seabed-source magnesium oil (most pure and least itchy) or ocean minerals magnesium oil sourced from filtered, deep Pacific ocean water. These are cleaner magnesium oils. They are probably far purer than nigari magnesium chloride, especially if it derives from the Sea of Japan (which contains many industrial contaminants). One source that offers these clean magnesium oils is Integrated Health:
Deep ocean magnesium oil itches a bit more than seabed magnesium, which is sourced from a mile-deep seabed lying untouched for 250 million years.
It took me about 2 months to adapt to ocean-source magnesium oil, so I hardly itch. I feel a slight sensation, but it goes away quickly. Yet, I prefer the ancient minerals magnesium oil the most. There is almost no itch and it's extremely pure.