If you must use the supplies, 13.8v will be okay but your current drawn needs to be low else the regulator will get too hot.
13.8v - 5v = 8.8v
If you were to draw 100mA this is 8.8v x .1A = 880mW needs to be dissipated by the regulator. ouch
You could feed your supplies to a buck converter set to 7 or 9v.
In the world of digital electronics, 9V and 12V are equally "weird" because digital electronics usually run at 5V or 3.3V. Even if you power an Arduino with 9V or 12V, it is not actually running at that voltage, it is throwing away the extra voltage as heat so that it can run at a lower voltage, by employing a linear voltage regulator. That's wasteful, and there is a limit to how much heat can be dissipated before damage occurs.
So it's better to directly provide the 5V or 3.3V the Arduino circuit requires. You could use your 12V supplies for this, adapting them to produce the lower voltage using a DC-DC converter such as the one suggested above. But beware! These converters can produce large amounts of noise in radio frequency bands, the enemy of the radio ham. Careful shielding and filtering can reduce that, but it may be simpler to abandon your 12V supplies and get new 5V or 3.3V supplies. But that also presents a problem: modern 5/3.3V supplies will likely be switch-mode rather than linear types, so, again, there is the problem of RF noise.
...you surely know about linear regulators, power supplies in general etc?
I've never been into radio, but my father used to be involved in HAM radio before his interests shifted. Back then some basic electronics training was part of the process of getting a license in the first place. Things have changed, apparently?
Is there another way to modify your 12V PSU to output 5V? Maybe if the transformers have other "taps" on the low voltage coil which output 6~7V, you could replace the linear regulator with a 5V equivalent? Could be a little tricky finding a linear regulator with high current output but low dropout voltage, I certainly can't suggest one, but my knowledge of linear regulator models is limited.
The reason to ask is the fact that the hobbyists should use low power (current rating usually < 2 A) PSU to avoid the erruption of smoke/fire in the breadboard due to possible short circuits (by mistake).
I observed people doing experiments with 5V supply of the PC and after a while they came up with total fire? They could not believe that the PSU would deliver so much power (5V x 13A = 65W); because, it is just a 5V supply!
That's why in UNO Board, the manufacturer has installed "Polymeric PTC Resettable Fuse 15V 500 mA" type high quality fuse in the 5V line to protect the PC and the user's hardware setup in case of possible shot circuts/overload.
Every wall adapter type 12V supplies I've ever measured were close to 12.00V. It's the larger supplies that are intended to charge batteries, as previously mentioned, or to power devices that normally run on lead acid 12V batteries, that produce 13.8V. It's a "float charge" voltage for those, and close to the fully charged operating voltage of such batteries.