Need more hardware information, paulineb. But the new slackellive-openbox-7.2 may someting to look into. It's 32bit and uses the package manager slapt-get, which was modeled after Debian's APT/apt-get.
I tried the 64bit version, slackellive64-openbox-7.2 on an old Dell Latitude D630 with 4GB Ram and SSD and was impressed. Salix devs came up with slapt-get. Slackel is derived from both Salix and Slackware. Doesn't use systemd. Here's a list of others that may work for you. AntiX is debian and so uses apt-get, as well.
Do you mean your wondering if APT can be installed on non Debian systems?
The commandline utility that comes with a distro was designed to interpret and run commands on the system and do dependency resolution. Trying to install another type of commandline utility would collide
with the other utility that's installed. I don't think APT would be able to be installed on a non Debian system anyway.
Non Debian systems use another type of package management system that are like unto themselves.
For example Slackware uses slackpkg, Arch Linux uses pacman and Red Hat uses yum.
If you are accustom to using APT you could run MX Linux which is Debian based and was designed for older computers.