There are many extant examples of historic Highland Targes that lack the center boss, and certainly the infamous "spike" projection, or any sign of there having been one originally. In fact, most period illustrations show the targe being used in the conventional manner of other shields, and not wielded like a Madu, Buckler or similarly handled shield. The greater simplicity of construction locally, in a region where industry was not at the fore front, is one major contributor to this have no doubt.
Although only one of many good sources, George Cameron Stone describes the Targe as a "shield with two loops in the back, in which the arm is placed" in his esteemed reference bible A GLOSSARY OF THE CONSTRUCTION, DECORATION AND USE OF ARMS AND ARMOUR In All Countries And In All Times. The most common method was to grip the second strap with the hand, together with the dirk held downward in the same hand.
My background is in Scottish Regimental, Clan, and Piping related pursuits, and as such I have a multitude of references covering this topic. I've quoted the above source simply because it is likely to be on the shelves of more casual military historians than the far more specific, albeit obscure, ones in my personal library.
In short, you may go with either construction and still be accurate, however one should not dismiss the more commonly found pattern in the process.