How to stitch up filled fish?
I would not expect chicken wire to be food-safe.

According to the FDA, to be considered food-safe, a material must meet several conditions:
It must not allow the migration of “deleterious substances or impart colors, odors, or tastes” to food
Be “durable, corrosion-resistant, and nonabsorbent”
Possess sufficient “weight and thickness to withstand repeated warewashing”
Be “finished to have a smooth, easily cleanable surface”
Have resistance to “pitting chipping crazing, scratching, scoring, distortion, and decomposition”

-marlinwire.com
Now a lot of that might not be much a concern if you only plan to use it once, but still, I'd recommend spending a few extra pennies for stainless steel or aluminum wire, which you should be able to find in any large hardware or home improvement store.  The link above goes on to say specifically that grade 304 and 316 stainless steel and aluminum are food safe.
Another option that might work for you is a grilling basket.