Provided your router has enough storage (e.g. external USB HDD), it shouldn't be a problem if you're familiar with the command line.
Your router is most probably running either an ARM or a MIPS processor. The appropriate debs can be found in the Debian repositories here. You can't install them directly on the router, so extract with
dpkg-deb -x filename.deb destination-dir first.
You can then try moving the extracted files to your router, and seeing if the binaries appear to work. If not, you can always (cross-)compile them from source. I don't see anything in
apt-cacher-ng that should prevent it from working on a non-Debian-based system.
Alternative: Use the OpenWRT packages
There's also an
apt-cacher-ng branch for OpenWRT on Github here, and it looks like it's being actively updated. DD-WRT runs on a superset of the hardware supported by OpenWRT, so it would almost certainly compile and work on your system. This may be the easier option.