Just asked dh as he buys all his work clothes on business trips to the US. He recommends Brooks Brothers, who have the shirts you are looking for (French cuffs and non button down collars) as well as suit type trousers. The shirts are fab as they are non iron (supima) but feel like cotton ... We live in a hot country where 100% cotton shirts can look wrinkly very quickly.
If the style you need is rare in the US, why not buy in the UK (Marks and Spencer / John Lewis etc) and ship to the US, then on to you? Might take a few days more but you'd know the sizing and what you are getting....
Just asked DH and he says that US men don't tend to wear shirts that you need cufflinks for hence why you' may struggle to get them. He's also suggested J Crew and Banana Republic - we live in a hot part of the States and this is where he's just been stocking up on stuff for the office
We live in Caribbean but can get stuff sent to USA mailing address and then shipped to us which is helpful because the choice of shops on our island is rubbish.
DH needs some lightweight/tropical weight dark suit-type trousers (but not suit jacket as nobody wears them) and cotton shirts without button down collars suitable for an attorney. Can anyone recommend a good online place to shop? He is 6'2 with 33 inside leg and wears UK size 17 collar but I have no idea how USA sizing works and whether things come up similar sized.