I'm running an old square taper 105 crank (1990s?) with 113mm Shimano BB with the chainring in the inner position that gives me about a 40 mm chainline...thats not perfect but its good enough. With a 2.5mm BB spacer, I can get a perfect chainline.
To get a better chainline with the outer position, you'd need a shorter spindle. Either a 107mm or 103mm spindle would probably give you an acceptable chainline.


I just remembered...I also have another bike with an early 80's Shimano 600 crankset and 110mm BB with the chainring in the outer position that gives me about 44mm chainline.

Also note that shimano BB spindles are not always bilaterallly symmetrical, whereas others, such as Phil BB spindles can be. Its not always simple to know what you need because two BBs with the same spindle length can yield different chainlines. What are the numbers stamped on the inside of the crank arm? That will help us figure out exactly which BB will work best.