You probably uses things just as 'dangerous' every day in your house such as drain cleaner, toilet bowl cleaner (some of which contain muriatic acid!)
Like Dave said, just use common sense and you will be fine. If you should spill any on yourself remember you can just jump in the pool to wash it off. Glove and goggles are never a bad idea when working with any dangerous chemical, bleach included btw!
The fumes are pretty strong and you don't want to be downwind of them. That is the main caution.
Also never add water to acid, always add the acid to the water. You can either pour it slowly into the return stream or dilite it in a 5 gal bucket of pool water first. Once it's dilutes there are really no fumes.
Besides the fumes dry acid is really no safer, when it dissolves in water it forms sufuric acid!
The way I add acid to my pool is I put the acid bottle and the plastic measuring cup on a plastic dinner tray (like you might find in a cafeteria) to catch any drips so they don't hit the deck, measure the acid I need into the cup, and either pour it slowly into the return stream after capping the acid bottle or, on a windy day, pour the acid into a big bucket of pool water so the fumes don't blow my way. I dip the cup into the pool to rinse it out. I have my hose nearby running so I can rinse off any spills or drips from the acid jug after capping it. If I spill any while measuring the tray catches it (hasn't happened yet but I have had some drips run down the acid jug into the tray instead of on the deck!). If there is any acid that did drip or spill into the tray I just push the whole tray into the pool.
One final trick, Opening the acid jug. They usually have a safety film over the opening when you first open them. I use a wooden skewer to pierce it a few times, dip the skewer in the pool to rinse, and use a gloved hand to remove the rest of the film. A quick dip in the pool to rinse off the film and you are good to go.
To dispose of the empty jugs i submerge them in the pool to fill them up and then empty them back into the pool (pour them slowly so it doesn't splash--remember there is still acid in there.) Once rinse out I toll them in the trash. Don't forget to rinse the cap off too.
One final safety note, remember to keep kids and pets away when you are using acid ( or ANY pool chemical for that matter!) I make sure my three dogs and cat are in the house BEFORE I break out the pool chems!
Hope this removes some of the fear you seem to have about muriatic acid and remember, this is just the way I do it, not the ONLY way.
BTW, if you are trying to lower your TA you should drop the pH to 7.0, then aerate to bring it back up to about 7.6, and repeat this until the TA is where you want it. Adding acid lowers TA, aerating brings the pH back up without bringing the TA up again.