Can I replace my shower controls?

It seems like every shower has its own unique way of controlling water temperature and pressure. Of all the showers I've ever used, no two of which have ever been alike, I like my controls the least. Plus the faucet has started dripping lately.

Is this likely to be something I can replace on my own, without a plumber? To me, that means: Can I likely do this without damaging the wall, without having to mess with pipes, and without needing to do anything involving words like "hacksaw", "weld", or "plumbing torch"?

Basically I believe in my ability to buy a faucet and control thingie from Home Depot; to use screwdrivers, allen wrenches, pliers, and regular wrenches; to use things like plumbing tape, lubricants, and caulk; and to remember to turn the water off to the house.

Would a project like this likely require anything more complex than that? I tend to prefer shower controls that have separate knobs for hot and cold, but I figure going from a one-knob setup to a two-knob setup is definitely going to require reconfiguring the plumbing. Should sticking with a one-knob solution be okay?

I don't know if it matters but I live in Florida in the US, and this place was built in the 1980s. I doubt this matters, but my current controls work by turning the larger knob left or right for temperature, and the smaller knob for pressure.

My place does have some annoyances - like the front door is an uncommon size that's difficult to find replacements for at places like Home Depot. Is there any chance of me running into issues like that when it comes to things like the size of the pipe openings?

Thanks for any insight.

Edit: Thanks for all the replies. It's pretty clear now that this is something that could very easily end up a lot more involved and time consuming and property damaging than I'm comfortable with.