Shootall,
Once they have broken into your house, they are gonna know in just a minute or so that you are a gun owner, whether you have a few on the wall or not, and they are going to tear the place apart looking for them.
Unless of course you keep your entire place sanitized, including having no hunting or shooting magazines or catalogs anywhere, and no trophies on the wall, and no reloading equipment or supplies in view, and no ammo boxes, and no head muffs lying around, and no cleaning equipment, etc. etc.
And, about 80% of American households have a gun in them anway, so they always look for them first.
So, I say, give them a couple of junk guns (with firing pins removed). Once they try to pawn those, they will never come back. :-)
Regards, Mannyrock