You can file for SS based on age, not when you retire from your job.
Now I have no idea about divorced filing, so it may not apply.
But if you are age appropiate for SS, then filing for it January of the year is better (according to other thread due to the increases). So if divorced filing works the same as regular filing, you could file in January, and even though work , they would just reduce the SS you get by a portion, (you still get some , which is better than zero) while you are working and waiting to retire.
Isn't it nice and complex