I am not your electrician, etc.
There are options besides gutting the room, if the conditions are right, and you are confortable doing so.
Is this on a floor with an accessible basement? Or an attic? If neither, then go back to watchwolf49’s suggestion (ETA or Heracles’ suggestion, although I’ve haven’t used one).
Turn off the breaker before beginning work. Test and verify circuit is dead.
In the switch box, you could connect the hot to hot, white to white, and ground to ground(bare to bare), with a tail off each, to connect to the switch from the hot and ground (neutral would pass by the switch, to the previous switched outlets and the new switched outlet). Cap and tape all connections. This will make the outlets live, albeit a long meandering circuit, but otherwise fine.
From the attic/basement locate the walls for the switch and outlet, run/fish 12-2 wire from the switch wall to the outlet wall into each of the switchbox.
Wire in the switch from the hot tail from earlier, and ground the switch with the ground wire. Tie in the neutral, bypassing switch, and connect the grounds.
On the outlet on the west wall, either a) break off the connector tabs between the connector screws, if you want to control one outlet, and keep the other live. Connect the switch to one set of screws, the live to the other set.
or b) cap off and tape the hot wire feeding the outlet, and wire in the switch, tailing in the neutral and ground to the old feed (to keep a continuous neutral/ground).
Test circuit with resistance meter with switch on and off to verify connections before turning on breaker. Be sure switch is off and nothing is plugged into the outlets when breaker is turned on to avoid surges. Test voltage with switch on and off.
If you are comfortable with spackling and wall repair, and don’t have attic/basement access, you could cut a small access hole above the switch and outlet where the wall meets the ceiling and proceed this way - IF the joists are running east/west. If you have a simple ceiling light (in another room) that you could take down, you may be able to see which way the joists run before cutting into the wall.