The new circuit does not have a 50 ohm output as the collector of the transistor has a high impedance output - much greater then 50 ohms.
(Forgive my ignorance in this area. I'm still trying to understand how to terminate a coax "at the transmission end".)
So you're saying that I don't need R1?
Terminating either end of the cable would ultimately mean you cannot drive the LED directly - you would send voltage over the cable to some kind of receiver that would drive the LED - as I said - it may be more complication then you need.
Where you might have a problem is the cable capacitance will attenuate the modulation to the LED. If, say, your cable had a capacitance of 200pF. Put a 200pF cap across the LED, and see if it still works as well.
If the capacitance is a problem with your current circuit, then you may be forced to move the LED driver to the remote LED circuit, and use s properly terminated cable to drive the input of the LED driver. In the case of your current circuit, it would mean moving U1 and Q1 to the LED, and sending "SIG" on a properly terminated cable.
I think that to make a true 50 ohm terminated connection is more effort then your application needs. Your first circuit looks fine.
(The current version has everything on one board. I need to move the LED to a separate board that can be moved around.)
So do you think I should just go with shielded twisted pair then?
I do prefer the coax with a unbalanced signal, but there is every chance that in practice a twisted pair would be adequate. We don't know the kind of modulation you are doing, but if it is sinusoidal type modulation, you will have no problem with higher harmonics. If the modulation is digital with sharp transitions, then you are more likely to have high harmonics radiating and you will have to be more careful with trying to damp the high resonances.
But if you have an oscilloscope, do a test. Connect the LED remotely via a coax. Connect the ocsilloscope probe earth to the sheils at the start of the cable. Probe the shield at the end, and if you have a problem, you will see the 2.3MHz. Then try it with a twisted pair.