Decorative swords have their place, they can look cool hanging on a wall for swinging in the air, I have seen some that are sharpened and since they are almost all stainless steel they will hold the edge fairly well.
I wouldn't swing any decorative sword around for any reason. The tang (is that the right part?) might be far too short and will probably break or slip out at the wrong moment. Google for the QVC moron that broke one into his shoulder.
Yes it is the tang that you are referring to, its size and how it is attached makes a huge difference, along with the type of steel used and the tempering process. Not surprisingly hand held weapons are an interest of mine.
As for the LARPing...see the attached. I still play regular games of D&D but I could never get into the LARPing. I guess the closest I have gotten was themed paintball outings.
In the chart I have to admit I fall down most of those branches to one depth or another.