If your 93 Caprice has its original water pump, common sense says to replace it as part of the radiator job. Replace the thermostat too, if it hasn’t been replaced in the past 5 years. Might want to replace all the rubber hoses too, esp if any are looking like they’ve seen better days. But definitely less work if you stick w/just the radiator, leave well-enough alone on the others. I can see it from that side too.
As far as stuck/broken fasteners, that risk can be greatly minimized by soaking each fastener with thread penetrant, apply daily for the entire week prior. If a fastener seems to have rust build up where thread meets block, try to scrape the rust bond away at that point the best you can with a steel dentist pick, as part of the penetrant spray work. Clean the fastener heads of anything that might slip before applying the wrench/socket. Start with a gentle force, not full arm strength. If fastener still balks in the reverse direction, try applying a tightening force first. Sometimes some forward/reverse force events over the course of a couple of days are required on really stubborn bolts. Tapping on the bolt now and again can be helpful too, not heavy duty hammering, medium force tapping, like with handle of crescent wrench. .
As for which penetrant to use, I usually use a combo of PB Blaster and my own home-brew. PB Blaster is faster, but my home-brew is better at really stuck fasteners. I put a little of both on. I’ve used Liquid Wrench before too, works nearly as well, but takes longer than PB Blaster.
My home-brew
1/3 acetone
1/3 Mercon 4 automatic transmission fluid
1/3 WD 40
@Bing’s idea to coat threads with something water-resistant before reinstalling can be very helpful the next time. I use moly-lube for that myself.
If you are inclined to try heat to unstick a fastener, not something I usually do, but if you do, suggest to do that before applying thread penetrant. The fumes from heating that stuff are not at all healthy to breath.
fyi, I replaced the water pump on my similar era Corolla about a year ago. Fasteners came off slick as a whistle, no problem at all. I did apply a little of my home-brew penetrant the day before is all. Most of the the bolts screw into the iron block on that design. Moly-lubed the threads before re-installing.