What? No that's stupid, you're stupid, VMWare is stupid. Hot-swapping hard disks? Sure. But that doesn't even require you to open the chassis.
Also, most halfway decent server motherboards these days come with dual NICs, so step 1 is to just reassign the IP to the other NIC port and plug it in. Or - and here's a mind blowing proposition - use both NICs with ethernet bonding! Wow, what a concept!
Anyway for all the talk of OMG DOWNTIME and these people being complete idiots, at least some of it has to boil down to them also being incredibly lazy and unwilling to go do the work at 4am. I've been working in the hosting/isp biz for a decade now, and downtime is just something that happens. If you can offload services to another existing box while the problem one is down, great. If not, you schedule some downtime and get to know the wee hours of the morning a bit better.
This whole concept of OMG CANT HAVE DOWNTIME is also just them giving themselves a hugely inflated sense of worth/importance. No, guys, the world won't end if some furfag in a far-flung timezone has to wait a few minutes for porn.