Hello,
I am web developer for over 20 years focused on PHP and Wordpress.
In order to transfer your Wordpress site to new hosting, I would need database admin access (from CPanel) on both old and new hosting, since that is the only way you can transfer Wordpress content.
If you check my profile here on Freelancer, you will see that I have a perfect 5-star rating, and one of my recent projects was Wordpress transfer.
Best regards,
Nikola