The significantly corroded part of this system is the 200amp main panel installed in 1966. This has the broken main breaker. When this main panel was installed, they wired the original fuse panel in a sub-panel configuration, and it has remained that way ever since. The fuse panel actually looks just fine and seems to work completely as designed, it's simply outdated technology that seems to be serving too many electrical appliances and circuits it it's present configuration.Is this the "significantly corroded" panel, or a separate fuse panel? If it's the significantly corroded old panel, I would tend to just pull and replace the whole panel and not continue to use it as a sub... I mean, if the main is busted, then you shouldn't keep using it as a panel--it doesn't take that much extra time to reconnect a few circuits. An inspector might or might not raise a question about it and refuse to let you restart it until you switch it out anyway.
If it's just a question of do you have to update your fuse-panel because you replaced what's feeding it, then there's usually no need to and most inspectors probably won't even notice, or if they do will be fine especially after you tell them you're getting rid of it in the next month or so.
It's very common to keep using an old panel, either as a subpanel or as a j-box with the fuses removed.
Disclaimer: not an electrician. They will probably be along shortly.
My question is basically, can I swap out the first part of this system and use that set-up for a short time, or do I have to replace everything when I touch one part of the system?