[here's one] that works with decora (rocker type) light switches (https://www.amazon.com/Master-Lock-Lockout-Universal-496B/dp/B001925P6W/ref=asc_df_B001925P6W/?tag=hyprod-20&linkCode=df0&hvadid=167150389150&hvpos=&hvnetw=g&hvrand=18441822094209114815&hvpone=&hvptwo=&hvqmt=&hv...)
You may not be able to find the breaker, but you can very likely find a light switch and switch lockouts are a thing.
You obviously have to be careful with that method because if it's a large space or a hallway there's likely more than one switch.
Other than that you're right to keep refusing to work hot. No you absolutely don't "have to." What this guy is telling you to do is an illegal labor law violation. Don't let people bully you into following their stupidity.
Thanks for all of your help!
I found something that works PERFECTLY.
https://www.amazon.com/gp/product/B001925P6W/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1
You can remove the inside toggles and it fits the entire power button panel PERFECTLY.
It leaves plenty of room for your fingers to mash buttons. I am going to use 3mm screws to install them without damaging the board underneath since the top of the controller is pretty thick.
While looking through his inventory, I ended up buying one of these with a small lock: https://www.amazon.com/gp/product/B001925P6W/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1
I'm hoping it's big enough and if the button can't fit, I'm just going to rip apart the inside until it fits haha.
If all else fails, perhaps a locking cover plate will fit over the timer switch.
Something like this: Master Lock Universal Wall Switch Lockout https://www.amazon.com/dp/B001925P6W/ref=cm_sw_r_awd_K5CRvb7ZJAZB0
My power button is on the top of my case and I put one of these over it to prevent the cat from turning it off. Works great.