Cisco stacked 3750 switch

I have a stacked Cisco WS-C3750X-24T-L    switch, two of them in this stack.  They have dual power to a Cisco 2200 redundant power unit.  It appears (according to tac) that the on board power unit on the second switch in the stack has failed, and the 2200 is what is keeping it up and running.  They told me the onboard power supply is not hotswappable, and the second switch in the stack must be replaced. 

What is the best way to do this ?  Do I shut down both switches, swap out the second switch, plug cables back in and power up ?  Do I just shutdown the second switch with the failed power supply, pop in the new one, plug in cables and power up ?  The cfg is on the first switch in the stack correct ?  Is there anything I need to pull off of the second switch ?

^ second that.  If the firmware levels do not match, you may end up with a brick.  The master may attempt replacing firmware.  If it is writing old over new...brick.  If it is writing new over old, but stalls/fails...brick.

Better to do the firmware upgrade offline, while the existing stack units are still functioning.

In general, watch cable position.  Label them accordingly before disconnecting.  When you unplug them, all ports may not be equal.

For instance, did you have one forced to 10Mb duplex, or aggregated with other ports.

When replacing, I was able to move the downed switch 2u down, and mount the replacement.  Then I could move the patch cables over one-by-one.

YMMV.  But it made it easy that I could  WS-C3750X-24T-S   replicate the cable layout and not have to change any notes or documentation.