If it were me I'd cut a section out all around the bad section - I've tried the syringe injection with limited sucess over the years. For one thing, it's hard to get the skin to go down flush sometimes. And it's hard to be sure you got enough new adhesive in to rebond everywhere.

After removing the skin, I clean up the core and fit a piece of 3/32 balsa (assuming it has 1/16" skins) , then epoxy it in place. Final step is sanding the surface fair with the rest of the skin. For me this is a fast and easy way to get a positive fix.

One last thing. I'd go some distance beyond the faulty area to make sure I got it all.

FWIW