The following information is reported from ASM Handbook Vol. 6:
ZIRCONIUM is a corrosion-resistant structural metal that has many physical and mechanical properties similar to titanium. The metals and alloys based on zirconium and tantalum have weldability characteristics similar to those of titanium. Zirconium can only be welded to itself or to other reactive metal alloys, such as titanium, niobium, or tantalum.
Both Ti and Zr can be welded to one another. Both alloys require extreme cleanliness and protection from contact with the atmosphere during welding. Here is some information to review;
I would consider an SFA 5.16 ERTi-2 filler metal with the GTAW process. The root and weld must be shielded at temperatures above 500 deg F during welding. In some welding applications, a gas tight chamber is used to assure prevention of contamination from oxygen, nitrogen or hydrogen gases for Ti and Zr.
I found the Wahchang site by accident last week. Useful technical references, but a bit short on welding info.
Go to technical information. Very cool picture at the top left as well!