Are there any side effects of using sodium hydroxide as a mold-cleaner in the shower?
I think you are right to use caustic.  NaOH is fantastic.  It comes with some positives that outweigh the negatives in your case.  Peroxyacetic Acid or Peracetic acid, they are the same, come with some things you should know about.

It's an explosive acid.  The guys who have jet packs and fly around.  They burn this stuff.  I have found that small doses dropped on the ground, can be very toxic in unventilated areas. I have been around for accidents where we were forced to clear entire floors of people for 2 plus hours for spilling as little as 8oz.
Just like hydrogen peroxide sold at your Walgreens, this stuff is the same, just much more concentrated.   Often the stuff in the store is sold at 3% and Peroxyacetic acid is often 25% concentrations of hydrogen peroxide. It also will have some acid affect on your grout and tile. I would be more cautious of acid on grout than caustic. 

Benefits of the Peracetic acid solution include:


Extremely short contact time needed to kill germs.  They use this stuff in chicken plants.
Breaks down into harmless vinegar and water given time.
Extremely small amounts needed at 25% concentration.  1oz per 6 gallons of water to create a sanitizing solution. You dont need much.  5 gallons might cost you 150 dollars.  IT will last for 3840 gallons of sanitized water.


Caustics include there own benefits. 


They are great at removing protein.  They are used in major brewing, dairy, pharmaceutical and other food production facilities. They clean things. Wet things. Mold like things.
When mixed with chlorine they can kill bacteria and mold, and work at a lower temp. Do not mix chlorinated caustic with any acid.  You will make mustard gas.
Do not use purple cleansers.  They are usually made with high concentrations of nitric acid which will also degrade your tile or concrete.  Don't mix purple cleansers with chlorinated anything.


Remember that straight NaOH isn't a sanitizer. It is a cleanser.  Most commercial examples are blended with a chemical that is probably known to someone to cause cancer. It has all sorts of industrial uses.  If you need to sanitize your bathtub, cause your are making gin or something you could sanitize it with H2O2.  I think that would probably be bad for your biom though and I don't think you should sanitize. Cleaning and scrubbing with high powered lye cleaner will do you just fine. Remember to rinse. Also remember to be soft on your grout with the brush and keep the temp on your wash bucket really hot. As hot as possible.  Most of that stuff is meant to work at 120-160+ degrees depending on how it is blended. Hot caustic means less scrubbing, more waiting followed by washing off.