A pressure balancing valve is typically something installed inside the wall, and it's not part of the shower head. I'm not a plumber, but I am unaware of any shower head that that will eliminate pressure fluctuations if you have that problem.

We replaced another shower and the pressure balancing valve was built into the tap. I don't do plumbing or electrical so I have to "trust" my husband and he told me that this is how it is. I don't believe that you can't install a unit to accommodate any shower kit. There are a ton of them online when I looked it up. Again, he said it has to be built in the tap. Maybe it's time to bring an outsider in to do this one task. All the plumbing will be fully exposed so access to the pipes won't be an issue.

It's not something you can just screw on outside of the wall. However, if you have access to the pipes in the wall, then they can be cut and a valve can be mounted. It's not technically part of the tap: the tap is downstream of the piping coming out of the valve. Unless you have excellent soldering skills and know what to do to avoid damage to the valve internals during installation, getting a plumber would be advisable.

Thanks Kudzu9.
He has done quite a bit of soldering - all of our renos are done by us and so far, no leaks, knock wood. I do like the idea of having options for the shower I choose because all the ones I like do not have balancer in it. I could improvise but.....nah.

That capability is called pressure balancing or "anti-scald". It's usually built into the control valve but there are also shower heads that close down when the water temperature is too hot. I think it's been a legal requirement for control valves for at least the last 15 years, maybe longer. It doesn't prevent pressure drops but it does prevent that resulting in a temperature change.

Unless you're in a multi-unit building with no control over the hot water temperature, I think the best way to avoid scalding risk is to turn down the setting on the water heater so that it doesn't get dangerously hot.

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Well, if he has experience like that, then it shouldn't be any harder than what he has done before. However, those valves can take a bit of heat to solder properly, so it is advisable to temporarily remove any internal valve seals or O-rings before doing the soldering. Also, if any of the copper piping comes into the valve from the top, don't overdo the amount of solder applied as there is a possibility that extra solder could flow out of the joint internally and mess with the proper functioning of the valve.