Those are good recommendations re pickups for your application
I'm not real familiar with Ibanez installs but I have seem some odd stuff regarding wiring, magnet polarity and cavity / feet design so I would check in with BKP on that.
It's always worth taking the strings off and getting some photos of the pickup mounting, pulling the pickups out (they are in their rings so leave them in those so you don't lose adjustment) and getting photos of the legs on those, get photos of inside the control cavity etc and familiarise yourself with the guitar before ordering anything. But definitely contact BKP to ask about the replacing the pickups.
Black Hawks are all short leg and string spacing is irrelevant because they are blades.
If you get a more conventional design like the Miracle Man you will need 53mm short leg, but check that there is nothing odd with the feet on your legs. If there is enough room in the cavity around the feet then the square feet of the BKPs should be fine.
I prefer to do a full rewire generally, right down to the selector switch, but be aware that the Ibanez wiring is probably a different colour code if you keep any of it
Schematics are on the BKP site