I haven't seen anything that would imply that construction factories could build anything aside from civilian space stations using the new skin-hull instead of armour, so the answer is probably that you would need to use shipyards. I already use OWPs for planetary PD whereas PDCs handle missiles, so I'm used to having one shipyard at 2000 tons with like ten slipways, that builds FAC/LACs and OWPs. You can make a simplistic 1 GC turret OWP for 950 tons and a pretty decent 4 GC turret one for under 2000 tons. Retooling isn't that much of an issue because you generally don't need to build both at the same time.
Ie, I build ten OWPs, then use tugs to haul them to their new home, retool for FAC, build a batch of 20 or 30, then design new the next generation OWP, retool for it, build new OWPs and rinse and repeat.