best scissors: normally I use regular sewing shears, but in a pinch, I've used sharp kitchen shears. the sewing shears have maybe 5" long blades, with rounded tips and will cut feathers crisply if they're sharp. and on a typical duck, it only takes 2-3 snips to get all the flights so it's fast and least stress on the bird. we clip one side (right) only, and primary flights only, leaving an inch or so of flights extending beyond the secondary feathers.
I've been lucky, I've never hit a bleeder, but I usually wait until the flights are fully grown in and I check the feathers for those still growing before I clip.
not so easy to do alone, better with 2 people for sure.
we keep Blood Stop on hand... I've never had to use it on a bird, but we had a ram knock a horn off and tear the growth ring around it and he would have bled to death if not for the combination of blood stop and me holding pressure on the wound for more than 20 minutes. anyway, it's good to have on hand.
glad your new bird is going to be ok.