Copying firmware from one switch to another?

I have a stack of cisco 2960x switches in production, and was just shipped a new 2960x to add to the stack. In the past I've had issues with adding a new switch to the stack if they weren't already running the same IOS.

The stack is running a fairly current version of IOS, but the new switch is running a slightly newer version.

Due to stupidity within my organization, my Director (who is currently on vacation of course) is the only one with a Cisco TAC login. So I can't simply hop on the web site and download the same image the others are running.

So what I'm wondering is - can I simply log onto one of the switches in my stack and TFTP the .bin file off, put it on the new switch and rock and roll?

My hesitation is that unlike the good old days when the IOS image was just a single .bin file, there are a ton of other files in the folder along with the .bin, like the files in the html subfolder.

Is there a recommended way to get the files off the old switch and onto the new? USB drive maybe?

Thanks in advance.