how to update 2 apple watches

Hello All, I must be missing something but I recently got a second Apple watch, and this morning while I set one on the charger, and the other on my wrist,

I tried to run the SW update for the one on the charger,

but of course due to wrist detection my phone had switched

and was trying to run it on the one on my wrist,

not the one on the charger lol

So I put the one on my wrist on the charger, and the other back on my wrist - oops - focus went back to the one on my wrist again

… so I left one on the counter/ off the charger and one on the charger and it looks like my phone is still making the one sitting off the charger the primary - since it was on my wrist last, and no update happening on either of course…

So, can I wear my Apple watch, while my second on updates on the charger? Do I need to turn one off? I feel like I’m missing something here… many thanks in advance!