OP Question: Given the above assumptions, what I would like to know
- How can I transmit without an antenna tuner?
There is no law requiring an antenna tuner. Most solid-state rigs can handle a mismatch up to about 3:1 SWR. Above 3:1 there is usually severe fold-back of output power (most modern solid state rigs) to protect the PA from damage. Fold-back usually begins around 2:1 though and I know it does in my own Elecraft K3. However, by the time the mismatch is 3:1, so much power is folded-back that you are probably operating a QRP (even under 5 watts) station so you should get QRP credit (assuming you were transmitting 100 watts to begin with).
But, you can have a perfect dipole and still have high-SWR problems. Case in point. My 80-meter dipole (part of 80/40 fan dipole) has a 1.7:1 SWR at 3.57 MHz. I designed this antenna to operate best on the low-end of 80. My penalty is that the SWR gets worse as I go up in frequency such that by the time I am tuned to 3.9 MHz, the SWR is about 4.5:1 which is not that good (though easily corrected by an antenna tuner).
Therefore, my low SWR antenna at 3.57 is no where close to low SWR at 3.9 MHz.
On the other hand, my 30-meter dipole (operates 10.1 to 10.15 MHz band) is almost flat across the band. SWR at 10.105 MHz is 1.28:1, at 10.125 MHz it is 1.33:1, and at 10.145 MHz it is 1.38:1. So, I can (and do) use my 30-meter dipole without any antenna tuner switched into the transmission line circuit.
So, by careful design (and testing after it is in the air) of a dipole antenna and trimming or extending wire legs as needed for your desired frequency, you can have an antenna that has no need for an antenna tuner. Alternative methods exist in using transmission line transformers but this is often more problematic (in my opinion) and it does not really change the bandwidth of lower SWR you have to operate safely.
My examples are drawn here from my own experience with wire antennas because those are the most popular and they are my favorite. I do a lot of portable operations, especially when on birding photography trips with my wife (the photographer) I will set up a portable station out in the middle of nowhere using (usually) wire antennas I launch into trees with a sling shot. My SWR is NEVER good in these situations. I have no intent or attempt to create a low SWR resonant antenna. Instead, I make sure my transmission line is reasonable efficient and short (under 50 feet) to limit the losses. My rig most of the time is an Elecraft KX3 though I also use a KX1 and the Norcal 40A. Mode is always CW. Power is always QRP.