I'm building up an old Terry bike and will likely pick up a NOS Shimano 600EX FC-6207 crankset. The corresponding bottom bracket for this crankset is the 116 mm BB-6207 cup and cone. However, given the ease of finding a new UN54 cartridge compared to sourcing a BB-6207, would I be able to use the crankset with a 115 mm cartridge? My bike has 68 mm diameter English threads.
Yes. Remember that 1mm of difference is 0.5mm difference on each side and you will not have to adjust your derailleur or gears to accommodate that. Sounds like you have done your homework already.
But also be aware that offset is an important criterion. Cartridge offsets can vary from zero to 6-8 mm, IIRC, and you want to be within about 3mm or the cups won't be adjustable enough to maintain the proper chainline.