From the photo it's hard to tell, but if you put the fan where the register is, doesn't that put it really off center of the space? Again, hard to tell from the perspective.
I wouldn't do wall registers. Way more work in framing and ductwork. Do you have attic access or no? I'd either do three way vents on one side of the room blowing across the room, or four way vents more centered in the space. A good HVAC contractor should be able to give you the ideal location for the space, considering exterior walls, windows, seating, etc.. The nice thing about the round registers is that you get less of an air current or a strong draft under the registers, I think they more evenly distribute the air. The stamped style seem to be more directional and you'd defiantly feel the current when the system kicks on.
We have a 60 year old house with round registers. I initially wanted to change them because I am more familiar with them he stamped, but my HVAC contractor convinced me to keep them, and I'm happy I did. These no real noise that comes from them and with two in our living area, you don't really notice when they do kick on regarding drafts.
In my opinion, converting to wall registers would be a large expense with no real return on investment or advantage in airflow.