You could probably do this job yourself but, if you don't feel confident about doing this, have a competent gunsmith do it for you. The size you want would be the size of the bullet that drops through your other 686(with little force), that would also be the size of reamer, to look for.
Are you sure the chamber throats are you problem? Maybe call S&W and talk to them about your concerns? They do have an excellent customer service department and track record of fixing what ails a customers gun.
Steve