You could circumnavigate in almost anything. The odds of completing the trip go up with the quality of the boat. A true offshore cruising boat would means different things to different people. If you look at the different custom boats built specifically for certain cruisers you will find them built out of steel, aluminum or even cold-moulded. They generally have small cockpits, a rugged sail plan and heavy duty rudders among other attributes. There just isn't much of a market for cruisers as experienced wealthy cruisers are fussy and particular. Some will want fin keels and some long keels. Some Ketches, some Cutters ans some want Fractional rigs. Note that for day sailing and close to shore you would want large cockpits for entertaining or racing, large interiors for dockside pleasure and fiberglass for light weight, ease of maintenance and manufacture.
There are a few builders that come the closest to a true world cruiser. I don't know them all but a few are Amel, Valiant, Westsail. Others will chime in on some they know about.