The design of the crank itself is one of the most significant factors in determining the spindle length that you need. Never-the-less, 3mm difference is roughly about 1 1/2 mm per side. That's not very much. There's a good chance that the shorter spindle length will work without your chainring rubbing the chain stay or creating chain line problems.
If it was my bike and I already had the parts I'd definitely put them together and see how they work. If I was buying new parts I'd hold out for a 116 mm spindle.