It is fine to shorten the sleeve at the bottom. The buttons will be sewn on again the proper distance from the bottom. The old holes will come out with water and steam. The only thing that changes is the opening vent of the sleeve gets shorter because there is no cloth above the vent to raise the vent unless you taper the sleeve a bit. Sometimes when shortening the sleeves that much it is a good idea to taper the opening as the sleeve is wider at the top of the vent than at the sleeve hem.
Despos is a well known tailor in USA.