A decent tailor should be able to take the shirts in for you without adding darts. To do this properly, they will likely take in the side seams all the way down to the sleeve cuff. This should work well, provided you have a little extra room in the chest. Check with the tailor to see if they can take it in more at the waist than the chest, if that would cause an issue for you.
My problem/concern is that I am wider around my chest than around my waist. I would assume this is the case with most people? e.g. the BB extra slim fit is perfect around my chest, but it is baggy around my waist. Is this only remedied by darting or could it have been made differently?