The GT 610 will work on the 220 Watt PSU just fine, it hardly uses any power. The 300 Watt requirement is Nvidia covering themselves for the cheap no name Chinese firecracker PSUs that can't deliver the wattage they promise.
Having said that, the GT 610 is an incredibly weak GPU, it's only going to be about as fast as your integrated graphics. If you are looking to upgrade for gaming purposes, you'll need a better card and a better power supply. I think the best low profile card available right now is the GTX 750Ti, though we might be seeing some low profile GTX 1050s soon. Either card will need at least a 300 Watt power supply for real. Assuming Dell hasn't started using proprietary PSU connectors again, you should be able to find a...