... is to talk to someone at a local nursery, university, or landscaper/pruner. The way I know of trees whose roots grow near the surface is that their source of water COMES from the surface. Other trees have deep roots because they search DOWN for water. (I think Cottenwoods are an example of the later.)
Since Oak trees grow near the surface, their root systems extend about 3', either side of the leaf-line. The leaf-line is the line you'd draw AROUND the tree while walking under the OUTER-most set of leaves. And it's 3' on either side of that line that the most SENSITIVE roots exist. I would bet that by 'cutting' one of them off wouldn't hurt the tree unless it's a really old one or very sensitive. BUT, if you have to cut back a few roots, you may very well kill it. Find out about the root system in the library, and go to one of the aforementioned 'places' for more info.
As far as finding a reputable contractor, talk to the folks at the nursery, university, or landscape office for someone to be recommended. You probably should trim the tree way back too, but again, check w/your 'source of info'.