John, Steaming is definitely not going to do it. Steaming will only bring back fibers that were dented, not torn like in a cut, or sharp dent.
They now sell wood filler in different shades that is stainable also. Try and match it to your stock, a little lighter is better, because then you can stain it to match. Use a thin flexible plastic putty knife, and fill the holes and then use the putty knife to level them to the stock. You might have to do it again, because the filler might and probably will shrink. Do it again, and make sure you use the putty knife to level it again.You are using the putty knife so that you don't leave any excess filler built up on the stock, because then you will have to sand it. Let dry and see how the match is. They also sell markers for patching up scratches in furniture that will help to blend your color in.
If the finish to the wood needs to be done to those areas, post again, and myself or someone will help you melt the existing finish over to the new areas with just a small amount of time and effort.


David