I agree with the others on all of their points. As a protection specialist but new to K9s I am adapting my tactics accordingly. Here are some of my thoughts.
1) It is better to keep the weapon hand free. My leash is generally in the left hand only. My gun, and where permitted, club, knife, flashlight, etc, are all accessed with my right hand. I may switch hands and use both when putting the dog "on guard" (e.g. right wrist through the leash loop and holding it, and using my left hand too).
2) Without a dog or a weapon, if you strike first, you are the aggressor. Perhaps you are authorized by law, perhaps not. Consider the consequences of action and inaction.
3) Fighting stances vary. I prefer being square to the target. My firearm or my dog are at the ready on either side. Before having a dog I may have bladed to the left (left foot/support side forward) in a weapon retention scenario, but if I have the dog it's a moot point. Who would foolishly attempt to take my gun when I have the dog? Some dumb ass might try, but the dog is there to assist. As stated previously, the dog will react if I am touched. While facing the target (or bad guy), my vision is at least 180 to all sides. In a fight ring I only have to deal with one guy. In a street fight I need as much tactical vision as possible. So face to face seeing 180 or better for additional threats.
4) Security Professional as opposed to Fighter. Two different sets of rules of engagement and legal obligations. As a security professional or simply for personal protection hand to hand is my least desirable outcome to an altercation. I have a dog and carry a gun. I prefer to engage at a distance with either one. I risk injury in a close fist fight. I mitigate that risk by avoiding the fight - when I am just protecting myself as a private citizen. If protecting someone else, well then, I may be forced to engage but there are legal rules for that. For LEO, they have rules too.
5) Engage with a bigger distance. I am approaching this from a personal protection perspective, not a LEO one. I am either protecting myself or a client and do not wish to engage close up if avoidable. If I turn the dog "on", I may have to get closer to retrieve the dog after an "out", but the threat is most likely reduced or neutralized. From a private or public law enforcement perspective where apprehension may be required, there would hopefully be other officers present who don't have a dog. If not, then as I stated before the threat has been reduced or neutralized by the dog. In some instances you need to be just a handler, in others such a s LEO, you may need play more than one role.
6) State and local laws vary. In Texas, I legally carry a firearm and have a dog for my personal protection. To practice protection professionally, one must be certified by the state. The two are different roles with different legal obligations. Also, in different states there are different weapon laws. In Florida I can carry a club, but not in Texas. In TX I can carry a Taser, but in NJ I cannot. In NJ and some other states I cannot carry a firearm, but in 40 others I can. So my tactics have to vary with my location even for personal protection.
7) The dog and I are training as a team for the real world, not competition. There are things to learn from such competitions but I have to think of street survival first. I need to depend on the dog to protect my life, and I have to train to protect hers. We train together for our mutual street survival. The dog needs to be trained to be effective in fight with a human and survive the fight. In the future when we start training for room clearing and other scenarios, we will train to protect each other accordingly.