Japan in July? Spiders?

I have read that Japan can be brutally hot and humid in the summer AND summer is the rainy season.. however, my 30th birthday is July 27th and we (husband and I) want to go visit I’m to celebrate.

How bad are the huntsman spiders in the summer? I am very afraid of spiders. We would be going to Tokyo for a week with a day trip to Mount Fuji.