I would say to use coax lines with BNC plugs attached, the signal level is pretty small. Also, instead of a transformer and voltage divider, how about a cheap microcontroller operating as a sine wave DDS with a RC filter to filter two opposing PWM outputs? Then it can be battery operated and variable frequency.
A good idea, I have a DDS module here, but the very purpose of this thing is to keep it simple for me, and keep my focus on fundamentals. Once we introduce micros into it, we wander off down the side lane which is the insanity of software, and all that nonsense - I am trying to learn about component characteristics, not how to write C code or learn a new SDK

Computers and digital garbage is already too much in our faces all the hours of the day, and I am already on the PC too much, and so this HAS to be analogue only, if for nothing else, than for the most crucial thing - MY SANITY

I like to K.I.S.S. - thanks for the suggestions.