It's not even that complicated with hardware of that era.
Let's say you are afraid to destroy the through holes of the multilayer PCB by de-soldering the broken parts, or heating bordering parts up too much, whatever.
In most cases you can pull the caps just off from their pins, clean the pins, (even with paper tissue only) and simply solder the new ones to the old pins still anchored in the board.
Once I discovered "desoldering needles" I basically stopped being scared of desoldering through hole parts altogether. You can get a set cheaply on aliexpress or amazon or whatever.
You slide the needle over the component leg and then melt the solder. The needle slips over the component leg. Wait for the solder to cool and pull the needle out. Hey presto the leg is separated from the PCB pad. Also works great for cleaning solder out of a hole after traditional desoldering.
Indeed, don't throw out old boards due to bad caps. I'm working on building a recapping skill so I can keep my old hardware alive as well. It's pretty cool to have the ability to take old non-working or marginal hardware, apply heat and modern capacitors to it, and make it stable again.