I used doeskin (real doe skin) 'mits' with leather 'inner pads' for my hunting dogs to save foot pads being cut by sharp cut field stubble, etc.
The does skin is for anti-slip, the inner boot is to stop penetration of the pad. The smaller and lighter in weight the better but dont bind the 'ankle' joint or the dog will refuse them.

Some dogs will tolerate them, others will refuse or will walk/run as if they are walking on hot coals and broken glass. Best is to put only one on until the dog gets used to it (back foot first) ... around the house/home, etc. and when the dog is comfortable and ignores the first bootie, then increase to 2 then 3 then 4 ... then 'outside'. As with all things 'new' to a dog, make a happy game out of it and with lots of praise.

Yup, razor clam shells like one finds in Georgia, SC, etc. will slice a foot pad quickly and deeply. Get some 'bandage material with clotting enhancers' ... accelerates the stoppage of bleeding (not for use on cats).

Such 'booties' are great in Bahamas & Caribbean areas that have the ultra-nasty 'sand spike' / longspike burrs .... very painful and very difficult to extract from pads - they're barbed and VERY sharp.