One can sometimes find GREAT men's shirts at thrift shops for $3 to $5 that look new or almost new.
If you are determined to do this - I would split it up into the sleeve and then put a contrasting color in it so it would look like it was meant to have a piece on each side.
Oh, oh - you said DRESS shirts -
I really think that alteration would look dorky - and if he needs to wear a dress shirt, it probably should be one that fits relatively well.
Or get him a belly cincher - if a woman was wearing it, it would be called a girdle or body shaper.