With a business suit I sometimes (say once a week) wear a double-cuff shirt with cufflinks.
Unless the various makers I own shirts of all have an exceptionally wide fit for the cuff, which is unlikely, I must say I never had any major issue with fitting a watch beneath.
Of course I don't choose the bulkiest ones (i.e. no 11063), but a Viceroy or even a L5100 Carrera - with L5100 being infamously thick! - does not pose any problem.
Cheers,
Fabrizio