I know that power cables can sometimes interfere with network cables. When routing cables it is best to separate the power from the network cables.
When using a cable management arm (like below) can I route both the network and power cable through it?
Yes.
Even in the case of unshielded cables and "dirty" power, I've yet to see it cause a problem. The interference generated by the power cables is small enough that it doesn't interfere with the digital networking singles going across your RJ45 cables, especially over such a short distance in the cable management arm. And I've seen 4 power cables, 6 CAT5 cables and a half dozen cables for miscellaneous peripherals (SCSI, USB, serial, etc) all twisted together into one long mess without issues.
Analog may be another story, but as long as it's digital, you're safe, whether the cables are shielded or not.
The only places I've seen where you have worry about interference from power source in networking cables are near really big power sources (like you'd find in a 5-ton AC unit, for example) or when running cables over the 100 meter standard "limit" for CAT-5.
I am by no means an expert but I was always taught that as long as you were using shielded category cable you can run them side by side. We did this for multiple servers in a full 42U rack without any issue. However we also had PDUs to make sure we were sending clean power in the first place.
for the small amount of cabling involved, this is fine.
i usually zip-tie the power to the bottom because once the power is in, it's almost never moved. for everything else i use velcro ties to keep the cables at the top of the arm. i do this more for convenience than separation, but it does give you separation, too!
If possible I'd tie the power cables to the bottom of the arm and the network cables to the top. Even an inch of separation would be positive. As mentioned above the lengths involved probably won't lead to many issues, but it could exacerbate issues with very long runs (i.e. through an IDF / MDF to centralized switches) or if there's interest in 10GE, which is notoriously fickle even with STP.