Reddit reviews Nano Sim to Micro/ Standard Sim Adapter + Micro Sim to Standard Sim Adapter

I'm not sure about the whole "Don't tell your Carrier thing but can't hurt to be safe. You should be able just to stick your current sim in. However because you have an iPhone 5, you have two options. Tell AT&T you need a new micro Sim Card. (which defeats the purpose of not telling your carrier.) Or you need to get a Nano Sim card to Micro Sim card converter.
Amazon has one for about $5 here. you can always search around for a better deal too!

https://www.amazon.com/Nano-Sim-Micro-Standard-Adapter/dp/B009AQLWMA

I get it, though. You're pointing out an inconvenience. I'm not arguing that it's inconvenient. I'm just cheap when it comes to stuff I'm not going to use very long. :)

What about something like this so you can use the note as a backup?

Actually, there's going to be a problem with this. The iPhone 6s uses a Nano SIM while the Note 4 uses a Micro SIM. So you can't just take the card out of one and put it in the other, because it'll be a different size. However, you can get an adaptor (something like this). Once they setup the iPhone with the nano sim, you can put that sim in the adaptor and put that into the note 4.

Nano to micro SIM adapter. Haven't needed to do it personally but pretty sure this would do the trick.