Run /etc/cron.daily from specific user

You are right, the jobs in /etc/cron.daily (and weekly/monthly, etc.) are always executed as user root but you can simply swith the user from within the script and call that very script again as that other user, including all supplied arguments (although there won't be any in a cron.daily job):

File /etc/cron.daily/my:

#!/bin/sh

# If started as root, then re-start as user "gavenkoa":
if [ "$(id -u)" -eq 0 ]; then
    exec sudo -H -u gavenkoa $0 "$@"
    echo "This is never reached.";
fi

echo "This runs as user $(id -un)";
# prints "gavenkoa"

exit 0;

When the script is started as user root it will detect so and re-execute itself via sudo -H -u gavenkoa, that is: as user gavenkoa. This requires no special entries in /etc/sudoers because root is always allowed to switch to any user.

The exec replaces the current process with the new sudo … call and never returns. That's why you don't need an else clause.