Do you run into problems if the pi resets periodically. Why use an external circuit to do this?
You can simply put the line in ".profile" file under user pi..
at now + 10 days reboot
The "at" command creates a list of commands that are executed at various times in the future. You can also add right in the command to make any time you want. If you want it to happen at midnight, ten days from startup, use...
at midnight + 10 days reboot
It will start 10 days after the next midnight.
The one problem is, you need to check the "at queue" atq , to make sure a reboot command is not in the queue before adding another reboot. If so, you could get an "explosion" of reboots. The at command create the queue as a file saved to disk so even on restart, at commands are still present so a restart and execution of a .profile script will create a second reboot in the queue.
If this is an adequate path to a solution, you can also look at the other "execute in the future commands in Linux (Unix). Batch and Cron are some of them.