My MIL had shutters that opened inside the window box, but she had pretty deep boxes, definitely deeper than the width of one panel of shutters. Perhaps you could measure your boxes and the distance (if any) between the window and the furniture, and then go try out some shutters in a showroom?

Our old house in NC had lovely plantation shutters in the front room. Beautiful. Light-filled. Very irritating because we could only open the one that was not in front of furniture. Five were behind the couches, plus one on the corner was still blocked by the couch. I had to make do with just the louvers. We were on the south face, so it was tolerable, but a north face or a more northerly location, and I would have hate them.

Look into having a split put in halfway up so that you can open the top halves wide open and have the bottom halves blocked by furniture. A friend had this done in his dining room when his were installed and it was a terrific idea.

I'm sure by this time you have resolve your issue with ordering plantation shutters. However, I will still answer for other viewers.

You said the furniture is right beside the windows. You can order shutters hinged so all the panels in the opening open to one side. Also, it may be wise to use a greater number of narrow panels which will reduce the space needed in front of the window to open the shutters.

Hope this helps.

Here is a link that might be useful: Horizon Plantation Shutters