I don't have geese but I had a bunch of chickens, and I'm a human doctor, and I'm sure a lot of the same ideas translate, both for people and birds! My first aid kit for birds would include:
Vaseline - helps to protect from cold, also a great general skin barrier
Blue kote (or some type of gentian violet spray) - old timey antibacterial and anti fungal medicine which stains whatever you spray purple (so you know where it went). It will stain fingers, wear gloves. Easier to apply than ointment
Neosporin
Coban (or vet wrap) and gauze and non stick bandages
A good pair of tweezers/pickups
Saline wash and big syringes or a turkey baster
Here in the US you can buy penicillin at animal supply stores. This is good to have
You can also buy ivermectin which is an antihelminth. I've used this in rabbits.
Depending on your confidence you could include suture, needle driver, etc. I think it would be extremely difficult to suture an injured bird as they will likely not cooperate. But I'm sure it could be done with enough hands.