You might try the 'Aluminum Braze' rod that is sold for joining Aluminum and die cast alloys. It has been discussed in these forums but I can't recall the name offhand. Heat is applied with a gas torch.
I suspect the alloy is near the Aluminum-Zinc eutectic, ( Zn - 6Al melts at 381*C or ~717*F.), and if so, it will melt at a lower temperature than the pure Zinc that you are intending to join. Pure Zn M.P. is 419*C. Less than 90% Zn melts above pure Zn.
If you are inclined to experiment for feasibility, the infamous HF has some for about $12 per pound. The brand name stuff is likely to be higher purity but is much higher price. There are also other suppliers.
This stuff:
http://www.aluminumrepair.com/aluminum_repair.asp
or 'HTS-2000 Brazing Rod'
...Judging by the melting range of 717-737*F given in the MSDS, it looks like it is only a couple % one side or the other of eutectic composition.
Never mind the 'proprietary composition' BS in the MSDS, the Al-Zn binary phase diagram shows the necessary data. I suspect that it would work fine for your application.
If you decide to experiment, let us know the results.
BTW, if you don't exceed the melting temperature of Zn, fumes won't be much of a problem.
Regards,
Dennis