Your instincts are probably correct, but there are caveats. First of all, do you have the dihydrate? What does the bottle say? Is oxalic acid dihydrate effervescent -- that is, does it lose its own water over time? What does the method say? If its been done wrong for a long time, and gives the answer you want, you can't just change to make it correct, unfortunately. You will have to verify that the method works the same.
What is, in fact, the difference in mass between solutions made with both molecular weights -- maybe the difference is negligible, or beyond your ability to measure? You can compute it both ways, on your own, as a check.