how to disconnect external hard-drive from dying iMac

I have an old iMac (2011) with an apparent failing hard drive. It doesn't boot up properly--makes weird clicking noises on start up then after a long time goes to macOS Utilities page. When I run Disk Utility the internal hard drive is not visible. OK, so the hard drive seems to be dead.

I have a Lacie external hard drive connected to the iMac running time machine backup. I want to disconnect the external to see if the backup appears undamaged (mainly, all of my photos are backed up here, want to make sure the photos still exist). However, I cannot eject/unmount the external drive from Disk Utility: I get an error message that the external disk is in use. I don't want to simply disconnect the external drive because I am afraid of damaging it and losing the photos. Most of the remaining files are expendable.

What can be done? Is it safe simply to shutdown the dying iMac, unplug the power, etc. And then unplug (disconnect) the external hard drive? I figure this is safe, but can't find confirmation. Everything says to eject first before disconnecting.

I have a replacement Mac on order. If I can get the external hard drive disconnected safely, I can copy the photos etc to the new computer when it arrives.