Yes, that will be fine. You may want to check it out after building, put some E-field inside the box and see if it's sensible outside, or vice-versa.
The other option is mesh screening, which can be quite fine, fine enough it shouldn't alias with the LCD pixels; but it won't be cheap.
There's also just plain old distance, if you don't need the E-field in front of the box to be small but merely at a distance, just don't worry about it at all; it's quite high frequencies where you need to worry about emissions from a hole, slot or cavity.
Tim