Presumably the 10 VDC signal is output from an amplifier (often integral w/ sensor, could be just an op amp circuit). That has high current drive capability, so it is hard for noise to exert itself on the signal lines, since that would need to be a lot of power picked up. I can relate personal experience.
At Westinghouse, we made portable instrument systems to test 480 VAC motorized valves. Strain gages were installed on the valve stems, with ~1 ft of straight unshielded wire about 2 ft from the motor and on-valve control switches before going into a shielded untwisted instrument cable (Belden or Alpha wire) run up to 35 ft to the amplifier and digitizer. The strain gage signals picked up no AC noise from the motor running. I attribute that to them drawing ~50 mA current at 10 VDC, which is 500 mW power draw, since a 350 ohm bridge which is "low impedance". The signal traces did show a glitch when a switch opened in the 120 VAC control circuit. Not from the 480 VAC contactors since those were in the Motor Control Center far away, so likely from switch contact sparks (aka Marconi's first demonstration of RF transmission, spark to spark). But, the techs appreciated those glitches as a time marker, so we didn't improve the wiring.
In later work at Aerojet on a large vacuum braze furnace calibration issue, I found the Type S thermocouple wires (~40 mV max signal) ran straight thru the 480 VAC resistance heater control cabinet. Those are straight unshielded wire (Type S extension wire). That was designed by the vendor. Amazingly, I found no AC pickup from that, though perhaps there was when heaters switched (no concerns). Again, I attribute that to TC's being "low impedance" (effectively a short circuit), so noise sources would require significant power to override the voltage signals (Seeback effect). Indeed, TC's run backwards (apply power) have enough energy to cool, as in the thermo-electric soda can coolers for automobiles.
Long ago, when I first worked with National Instruments hardware, I wondered that they ran the signals from the 5B amplifiers to the PC digitizer board using unshielded, untwisted ribbon cable. The reason that worked was that the amplifier outputs have much drive power, so are effectively "low impedance". However, I did use some NI (or similar) hardware which used special twisted ribbon cable or twisted and shielded (forgot the app). I once opened a precision "charge amplifier" for DC-accurate piezo load sensors, from PCB Piezotronics (or Kistler). They ran the input wires from the BNC inputs in the air directly to the charge amp input, using Teflon stand-offs, because routing them on a circuit board would leak charge. They were probably shielded too. Similar tricks with nano-ammeters, though forgot the details. Many precision PC acquisition boards have shielded boxes over the critical first-stage amplifiers.
Finally, my toughest shielding task was at Westinghouse where we had to qualify our portable system for Euro CE mark (similar to FCC requirements). I spent a week at a testing lab in PA where our system was in a room with a powerful RF antenna sweeping thru frequencies looking for noise pickup on our system ("Susceptibility" requirement). To pass the strain gage sensors, we had to play tricks with cable shielding. You generally don't want to ground a shield at both ends, to avoid 60 Hz "ground loop" pickup, but we found doing so improved shielding to RF emissions. The reason is likely due to higher impedance of the braided shield at high frequencies, so you need as many paths to ground as you can provide along the cable. The hardest to pass was our eddy-current sensors since they used large wound air-coil pickups to purposely sense EM returns, thus were designed to pickup RF. I recall we had to write our way around that susceptibility. BTW, CE mark is a self-validation and only requires keeping a report at a site in a Euro country in case you are audited. You see them on even stuffed toys from China, which are likely never audited. Brexit likely threw a kink since our report was kept in a UK office. In another case, I was setting up our system in Korea for a demo for government nuclear agency visitors. During setup, we were getting high AC noise on the strain-gage traces. I finally found they were using an AC extension cord which didn't have a ground wire (Euro-style 2-pin plugs w/ side ground), so our processing box wasn't grounded, and thus the cable shields weren't. I had them run a ground wire from our box and clip to the motorized valve, then the AC noise totally disappeared. Avoided a big embarrassment. I had warned them about that extension cable earlier. Anyway, we then went with the reviewers to a restaurant then karaoke club, like every night. Like in Japan, working there is more than a job, more like being in a Samurai group.
In sum, if your 24 VDC power is not suddenly switched and is low-ripple, I wouldn't expect any effects on the signal wires. Even if switched, amplified signals may not pickup that, but would have to test. Twisting is more effective than shielding to avoid magnetic disturbances, such as from current flow changes (B-S law), which is why most ethernet cables are UTP (also cheaper). But, 24 VDC might exceed some safety thresholds. I was once called by a young engineer at a USAF Lab I had worked, questioning the safety of some speaker cable I used to wire 24 VDC supply to a level sensor. I told her that I think speakers might see higher voltages transiently. Anyway, that was the only suitable cable I had at home and USAF procurement took over 6 months and multiple signatures from unhelpful Majors, but she was welcome to try ordering better cable. I know that 120 VAC is a safety concern, but perhaps some run it in the same cable with instrument signals out of necessity (perhaps robotics), probably in custom cable with special wire inside.
