I've never looked at an '89's lower ball joint, but my guess is it is of
the pressed in variety. The problem is, to press them in and out you
might have to remove the control arm anyway.

There is a tool for this, it's like a big C clamp of sorts with the
proper attachments for different size ball joints. Press the old one out
and the new one in. I did this on my beater car a couple years ago and
it was a pain because I couldn't get clearance for the tool. Eventually
I got enough stuff out of the way and found the right angle and got it
without pulling the control arm. Of course it was a fwd car and I didn't
pull a lot out. A mustang may not have this problem and just removing
the whole front spindle/hub and brake assembly should give enough space.