A patch job should be quite easy, you just need some neoprene cement and strong thread. For the patch itself you could look into using a tough rubbery patch (like you get on wetsuit knees), but that would be risky in that it could reduce the flexibility. The easiest would be to use 3mm neoprene
Sew it from one corner to the other diagonally from both corners, leaving the thread loose as you finish. Once the cross is done, take the loose thread from the two corners and sew the edges with it. After that apply the cement to the edges and lightly to the stitching to waterproof it and bingo, job done
I wouldn't worry too much about the cement being poisonous, as long as you use it in a well ventilated area it will be fine. Read the label, if it presents a serious problem then it will say. To be honest you could probably do without the cement altogether, I use it mainly to protect the stitching from abrasion but with strong enough thread that probably wouldn't be a problem. I have some beastly leather thread that you could probably strangle a wolf with!