Removing a woodpecker's tree

I've got a pecan tree in my yard that may need to be taken down soon as it may be unhealthy and it is too close to mine and my neighbor's homes to risk it falling. I'm having an arborist come take a look to see if that is necessary. My only real issue with this is that I'm fairly certain a Red-Bellied Woodpecker lives in the tree. If not, he's at least been a very frequent visitor for the last 8 years. I also have Downy and Hairy Woodpeckers on my property but this bird leaves horizontal lines of holes all over the tree which my, very little, research says the Downy and Hairy woodpecker don't do. My question is should I be concerned with trying to create another nesting area for this woodpecker if the tree has to go or would they easily find a new tree that is suitable. I have two very large water oaks. I'm in a suburban area but there are a few lots with larger trees like mine withing a mile or so radius.

TLDR: woodpecker lives in my pecan tree. Tree may have to go. If so, is there anything I should do to provide a home for the woodpecker?