For anyone reading this, I spent 4 hours searching through RS and Farnell for references.
I removed all the cable with impedance not being 120 Ohms, and searched for 22-24 Awg cables.
The one I find that suit the best this application are the following :
(If some of the specialists here could confirm these choice that would be great.)
Alpha wire 6413, 2x(2x24AWG), Impedance 120 Ohms, Outer Diameter 7.1mm, Temp -20 to 80, unshielded :
https://fr.farnell.com/alpha-wire/6413-sl005/cable-24awg-2-pair-slate-30-5m/dp/1746265?st=6413
Lapp Kabel 2170204T, 2x(2x24AWG), Impedance 100-120 Ohms, Outer Diameter 7.1mm, Temp -5 to 70, shielded (i think)
https://fr.farnell.com/lapp-kabel/2170204t/cable-profibus-par-metre/dp/3034318
And if you want way overkill, you can run two of these cable
CFBUS.LB.021, 2x20AWG, Impedance 120 Ohms, Outer Diameter 8.0mm, Temp -50 to 70, shielded
https://fr.rs-online.com/web/p/cables-de-controle/1854913
The last one is the only one that is purposely made for dragchains and to move.
I will try my luck with the first one.