Ok, I've started the project and removed the existing crankset and BB. It took superhuman strength to get the BB off, 20 years of grit and tightness. I measured my existing BB spindle length and it's 117mm. The crankset I was considering is 113mm compatible and I'd have to buy a 73x113mm BB (the Shimano UN55).

So my new question - will 4mm difference in spindle length affect my chainline too much? I know it's only 2m on each side, but I'm reading on some sites that it would probably affect shifting. And if it does, how would I fix that?