We have a schnauzer / poodle + unknown others mix. His hair is a problem for him. Way too thick and prone to matting. He loves a short haircut every couple of months. His is not a good mix plus his bark sets your teeth to hurting. He was an elderly neighbor’s pet and we took him when she had to go into a nursing home.
No haircut would be the cruel thing.
How kind you are to take someone else’s critter and care for them. God Bless you.