I am turning an 80's road bike into a single speed commuter for my daughter. I am replacing the old cone and cup bottom bracket with a new cartridge model. The three axle lengths available are 107 , 110, and 113 . I am installing a Shimano 600 crank. I am planning to use a 40 chainring that I have on the outside of the spider. I am wondering if I get a 107mm axle will it improve the chain line? or will it be so short that the chainring hits the stay? I am planning to use a redished road wheel and a singlepeed freewheel. Any advice from would be nice.