I can use
crontab -e as a normal user to edit my user crontab. Does anacron have any similar feature for individual non-admin users, or does it only have a system-wide anacrontab?
Add the command in your ~/.profile to execute when you login, or put it in a hourly cronjob to run on its own.
You don't need to worry about anacron running all its scripts every hour if you put it in cron, as it keeps its own timestamps of its last run in the spool directory.
See man anacrontab for more info on making your own anacrontab file.
Depending on the volume of affected scripts, you may also just use
Example with bash:
This saves you from having to maintain two additional files.