1999-04 have exhaust manifolds, it's why they crack and don't look too good.
I believe its 94-98 V6 mustangs that have them, my 1995 V6 has factory headers.
It's always better to just replace than it is to weld, the metals already weak welding it is just a temporary fix.
Look at some local salvage yards for a 1994-98 V6. There about as good as aftermarket shorty headers.
You could paint them while they're off too.