AFAIK it's a matter of output source impedance and cable capacitance per foot. In general I would guess that 40' would still work.
The older the machine and the thinner the cable the more likely you will have issues with frequency response and noise.
A tube machine, even with cathode follower output would probably not work well. I am guessing that all your prosumer machines and outboard noise reduction units, being of similar vintage, have similar output level and source impedance.
Why not listen with a good short cable in a temporary setup, then swap for the 40' ad see if you notice a difference?
I would not leave the braid shield disconnected on one end unless the wire you are using allows a "quasi-balanced" setup where there are either 2 center wires (like balanced cable) or some sort of dual isolated inner and outer braid shields.