Scheduling local lambda function

I have an application in which there is a Raspberry Pi as Greengrass Core and multiple ESP32 as Devices and together they form a Greengrass Group. Now, I want to have a local shadow update to a specific Device at a specific time. I implemented scheduling of lambda function with cloudwatch triggers and cron jobs but this will not work if the internet is down.

I was thinking of using cron tool (https://www.raspberrypi.org/documentation/linux/usage/cron.md) for Unix systems to schedule a local lambda function which publishes the desired MQTT message to local shadow service.

Is there any way to accomplish this?