That would be the approach I'd use to avoid the headaches of overlapping images in Word.

Here's a tip though: when you place the full-sized A4 image, Word will probably attempt to scale the image to fit within the text area (defined by the "paper size" less the margins). To get around that, use the Layout dialog to set the Size to 100%, and then the Position tab to set the alignment "Left relative to Page" and "Top relative to Page". This will place it in the upper left corner so it will properly fill the full page.

If you can print full-bleed, this technique can be modified slightly. Create your image with bleed, then set the alignment slightly above and to the left of the top left corner (i.e. horizontally "Absolute position -0.1" to the right of Page" and vertically "Absolute position -0.1" below Page". The negative amounts will place it 0.1" above & to the left of the upper left corner, so if your image was created to be 0.2" larger in both dimensions, you'd have a 0.1" bleed all around.

You can achieve the same effect for an image created at exactly the paper size if you scale the it to slightly larger using the Layout dialog's Size tab settings.

Note that not all printers are able to print full-bleed.