I didn't know about that stuff, but in a pinch, corn starch helps for non-emergent bleeds like single tooth punctures for example and for accidentally dremeling too far into the nail. It's saved me a few vet bills from Lucy being too rough.

Pet first aid kits are mostly a joke. They don't contain half of the stuff you need imo.

For dog-specific vet kits:

• Vetericyn spray, both regular and the occlusive one.
• 2% Chlorhexidine solution. Can make something similar to Duoxo with a 1:3 ratio of chlorhexidine solution to distilled water in an empty foaming hand soap bottle. Helps with some disinfecting and was what I used before finding out about Vetericyn. It worked great!
• Large gauze pads. Easier to fold and apply extra pressure with.
• Distilled water for rinsing off the wound initially
• Cornstarch if you can't get the styptic powder. Of course, don't rely on corn starch for major bleeds.
• Grooming supplies like the small scissors
• Tweezers
• ziplock bags for tick identification
• Stuff to induce vomiting in case they get into something they shouldn't.
• dog-safe antifungal ointments for thrush between the toes. Lucy seems especially prone to them. Add extra gloves so that you don't give yourself fungus from them.

This is more everyday stuff, but could be helpful:

• a well-fitted basket muzzle for your dogs that doesn't restrict panting. Dogs can get bitey when they're hurt. If your dog is normally super chill, then you probably won't need a bite-proof one
• Catch pole like from Ketch maybe?.. Never know.
• a bite-proof muzzle like Jafco if you have a larger breed or reactive dog.
• A car tether like this one and a well-fitted harness (my fav one) with a handle you can easily grab in the event that you need to go to the vet in an emergency. That harness saved my dog's life. I was able to grab it quickly.