You can change the setting from the WordPress Admin to show the update reminder message will hide only for only non admin users or Admin to.
- Download the plugin and unzip it.
- Put the ‘hide-update-reminder-message’ folder into your wp-content/plugins/ directory.
- Go to the Plugins page in your WordPress Admin and activate the Hide Update Reminder Message
- Go to setting->Hide Update Reminder Tab make the appropriate setting according to you.