Changing the drive on the NAS is for those that like risk and :
are 100% sure that they won't make a mistake removing the wrong drive,
are 100% sure than when you replace the drive the other drives don't disconnect
are certain that something else hasn't failed like you drive back plane or one of the "good drive" is actually also screwed and won't survive a power cycle.
Any of the above will result in total failure of you are using RAID5 or lower... so doing a backup would be the logical thing, however going at full rate could cause the drive to fail.
A rate limited backup is what I would do first, to the cloud to an external USB drive.
eg. rsync --bwlimit
and then keep away from the box until it finishes. After that replace the drive however you want, hot-swap it if your NAS supports that, power off, replace it or what ever.
If you backup to the cloud, remember that restoring could also take weeks to restore.
Good luck.