I wouldnt worry to much about the dogs getting hurt, and its likely they would rather chase and tree a large cat.
Depending on the breed and size for the dogs I would be at ease knowing they were along.
They use dogs to hunt and 'tree' coyotes, foxes, hogs, large cats, and bears all the time. The packs are not typically large as you still have to train and control all your pooches.
Pigs use large packs. The more the better; its just safer for the dogs. They use packs around 15 dogs give or take.
Pigs are the most dangerous game to hunt with dogs. They lose dogs all the time (remember these are not just pets they are a lively hood for the hunters so while sad, its also life.. Its not often you hear of people losing dogs to foxes, bears, or cats... However a few poor hunters loose their small beagles to coyotes while they are out hunting rabbits.
For rabbits we use one dog (13" beagles are the bomb for this), some guys use 5 or 6 but it just makes it sound cooler.
Coyotes and foxes you run around 6 or so dogs. Foxes you can use little hounds, coyotes you use the 15" plus beagles or foxhounds... typically.
Often for bear you run a pack oflarge hounds like 3-6 dogs.
Bobcats and Lions are better for smaller packs of large hounds. 2-3dogs typically.
I was always told 3 dogs if your training (as in two old dogs and a young dog) and 2 if you want the animal caught. (as in you only need your two best dogs to tree the prey)
The louder the dog the better.
Usually unless you hunting foxes you use a type of coonhound (well for pigs they usually use a catahoula which is a type of hound) or coonhound cross. There are a number of coonhound breeds, the most popular being the Black and Tan Coonhound, Bluetick Coonhound, Redbone Coonhound, Plott Hound, and Treeing Walker Coonhound.
They are not super large dogs, and often are slender and not heavily built.
...anyway back on topic