How do I replace an outlet?

The added wires from the one working without the switch GO TO THE SWITCH. the wires in the part that works with the switch come from the switch.
To delete the switch just cover the wires that are on the switch return with approved twist on caps. and do not break the 'bridge' on the side of the outlet... you are set to go. (I personally would leave the wiring in there pretty much alone, except to make both normally on.. so if you want the switch back someday)
Another issue?? The use of red wires is part of the 220V system. When the power comes in you have a 120V leg+ and return,a 120V leg - and return
If you connect up the two (- +) and ignore the return wire, you get 240V for appliances.
IF you use one leg white/black for part of your system, and the other leg red/white? Then you can have problems IF SOMETHING GOES WRONG: because a 'potential' 220V current could arise (220V is way more lethal than 120V)
And even if no iternal equipment fault arises, you diodes will be happier on a single 120V line
You can check to see if you are using the two legs of the electricity.
Using an extension cord and a multimeter (cheap one for $10 will work) set for AC voltage range at least from 0 to 240V
Run the extention cord from one wall outlet you plan to use, to the other: then measure the electrical potential in the slots by cross measuring the four possible connections:
Say the outlet prong hole are A B C D
normally you use AB in one outlet and CD in the other.
Measure the voltage thus
Check AB (certainly 120V or near it)
Check CD (certainly 120V or near it)
Check AC (may be zero, 120V, or 220V)
Check BC (may be zero, 120V, or 220V)
Check AD (may be zero, 120V, or 220V)
Check BD (may be zero, 120V, or 220V)
NOW, if ANY were 220V... bad idea to use both outlets in one system. The different outlets are on different legs of the incoming power.
If NO combination gave you 220V, you are safe to use both in your setup.
The various ZERO or 120V combos do not matter in this test for 220V
Good luck!

Thanks for the info Elizabeth.

Great post, Elizabeth!
I also routinely replace dupes live, even showing my 16yr old daughter while doing it. Yet I remember as a kid I was fixing an old transformerless 5-tuber in the basement, poking around live with my requisite one-hand-behind-my-back to avoid closing a circuit, and suddenly woke up 10 minutes later 10 feet across the room, on the floor with a bruised head. Next day I noticed a small red mark on my neck. Later I returned to my basement lair, finally noticing the dangling piece of 16AWG clamped to the cold water pipe! "How convenient!", I had thought when installing it some months before....