Great idea but keep it simple! This really should be a first aid kit and not a mobile veterinary surgery.
Essentials are a couple of simple, sterile, dry dressings, a roll of cotton wool, three open wove bandages and an outer dressing, for obvious stop the blood/keep it clean/support it reasons.
Beware the stretchy bandage put on too tightly which will cause death to a limb!
A pair of curved ‘mayo’ scissors is essential as they can safely cut hair without damaging skin, and tweezers are vital for removing hair and debris.
A spare slip lead also helps as it can double as a muzzle for the nippy bits.
Remember always, ’first do no harm,’ so wounds should be flushed with copious amounts of saline (clean water will do) and not disinfectants/antiseptics etc, which cause cellular death.
There is therefore little point in carrying these although some basic hand wash for the operator is useful!
Skin glue, a stapler (and staple remover), ocular lubricant, some pain killer and a professional tourniquet can be useful additions but I would speak to your friendly vet for some basic instruction on how these can best be used.
The latter, for example, is handy to stop bleeding for up to 15 minutes as you deal with a wound.
You may be surprised that your vet will probably be delighted to supply all this at a reasonable price.
I would certainly rather know that my clients used the right stuff safely! Oh and a mobile phone.
I get sent plenty of photos of wounds these days with requests for advice!