[G0HZU_JMR]

If you don't want any active parts inside the sig gen then the other way to do it would be a series resistor of maybe 4k7 ohms and a DC blocking capacitor fed from the cathode feeding into 50R coax that then exits the sig gen.
At the external counter end of this coaxyou could put a wideband 50R gain block to drive the counter because the level out of the coax will be quite small if you try this option. But the frequency response of this will be very good as long as the counter end of the coax is terminated in 50R by the wideband amplifier. This passive solution will load the cathode a bit but I'm not sure it will matter much.

This method is worth considering if there is a fairly big RF waveform at the cathode. It would be viable if there is maybe 5Vpkpk of RF at the cathode?
The 4k7 series resistor and the 50R coax will act as a very lossy potential divider but the wideband gain block can make up for this and drive the counter. I would use a couple of small 2k2 resistors in series to make up the series 4k7 resistor in order to minimise the overall through capacitance here. But 0.25pF package capacitance across the 4k7 will act as a pre emphasis up at VHF so maybe the capacitance doesn't matter here?