Electrical – Baby proof 240V outlet(for air conditioning) in living room

IMO it makes absolutely NO sense to use an existing circuit, especially considering how taxed they are. As long as your panel will accept tandem breakers what is the issue? Also, with a house of this vintage I highly doubt the wiring is grounded, which you cannot extend. And do not assume if the wiring is old AC/MC cable that it is grounded, much of it from that vintage is not, regardless of the metallic sheathing. The only metallic wiring like this that can be used as a grounding conductor is that with the think aluminum bonding strip running along side the insulated conductors. Besides, you never know what you might use this new receptacle(s) for. Don't think you'll never use it for anything more than a laptop charger.

Also, you re-purposed the old A/C circuit for a dryer?? Was it at least 10/3 cable? If not you have a non-complaint and potentially dangerous circuit if used for a 120/240V electric dryer.

Change sockets too

When you change the circuit voltage, simply change the socket also. Your normal common Mr. Horrorface socket is called a NEMA 5-15. You will simply be replacing it with Mr. Nope, aka a NEMA 6-15. They're common as dirt, every hardware store has them.

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As far as your power cords, if you can't find a C13 to NEMA 6-15, you're just not trying very hard. I found it ridiculously easy, try it yourself. Your 6A device (<= 1440 VA) should use a NEMA 6-15.

The NEMA 6 family has the same rules as the NEMA 5 family: the 6-15 plug will also plug into a 6-20 receptacle, and you can use 6-15 receptacles on a 20A circuit as long as there are at least 2 sockets on the circuit.

Only use 6-20 plugs on machines which actually need more than a 6-15 can supply, i.e. 3600-4800 VA non-continuous or 2880-3840 VA continuous. Such large loads are not a good match to the IEC C13 connectors, because they were never intended for near-20A current. Such large loads would use a burly connector like NEMA L6-20.

So go buy the right cord - they are $7 - or just lop the plug off a C13/5-15 cord, and attach a 6-15 plug. Don't know what your hardware store charges for those, probably $4. As far as resellability, lots of bitcoin miners want that stuff.

If you are sweating bullets over a $7 power cord, then your cheapness is an accident waiting to happen. If you do not want to spend money on plugs and sockets, them simply lop the plugs off, buy $1 strain reliefs and hardwire them into 4x4 junction boxes.

Also, don't rely on the Internet for pricing electrical gear. No wonder you're getting sticker shock. Everything on the Internet is stupid expensive because they are generally low cost parts that are expensive to ship. Talk to your 3 nearest electrical supply houses and tell them you're buying a lot of gear and not happy with the prices at Home Depot. Or the advice.