I’m sure you’ve done your research and weighed up the relevant factors regarding the timing of your surgery, and you sound confident in your decision to go ahead. I imagine your disappearance from the work scene will be less noticeable in the present restricted circumstances.
You’ve discussed it with your family - they’re the ones who matter. You don’t need to tell anyone else.
But if people notice, and ask you, you could choose to be open about it, after all, it can’t be that unusual in the beauty business. Speculation and gossip spread like wildfire in those circles. You might prefer to be upfront about it. People will be genuinely interested and probably very understanding.
On the other hand, people may not notice anything drastic and might just think you look really well.
Don’t take any risks with your health and safety though, either with regards to Covid, or the procedure itself.