Problem migrating a WP site to other server

Hi,

i have to move a WP site to other server and i am getting some problems to make it work. My main problem is that the MYSQL version supported in the new server is older than the new one – yeah, it’s ironic and stupid but i have to. My problem is with the famous utf8mb4, which is not supported for the new server. I tried a DB Migration plugin but it crashes all the site. I tried also to import the DB with MYSQL40 compatibility and this works, or that is what i think. When i try to log in the WP site un the new server, WP notice that cookies are disabled because a problem occurs. I was looking for a solution to all this mess but i’m at a dead end. I hope all of you guys can help me. Thank you and sorry for my english.