There are different cyanoacrylate formulations for humans and animals. But the idea is that you close the wound and then apply the glue to the skin above the wound to hold it together. You shouldn’t be getting glue into the wound.
I’ve found a quality butterfly bandage with strong adhesive does wonders… better than steristrips and skin glue for sure.
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Quick search on Amazon resulted with some skin staples. Could be an alternative for you.
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