ShipStation allows you to adjust the scheduled Ship Date for a shipment when you create shipping labels.
If you notice that you're typically doing this after a certain time of day, you're also able to specify a cutoff time, so that ShipStation can roll that date forward for you automatically after that time's passed.
Head to your Account Settings (the wrench icon in the upper right).
Next, select Printing and then Printing Setup from the sidebar on the left.
Look for the row related to Labels, and click in the Document Options link in that row.
In the new window, scroll down to the "Shipping Cutoff" section and check the box to enable this feature. Adjust the time as needed, just keep in mind that it will refer to the time zone set in your Display Options.
Don't forget to Save Changes!
Going forward, shipping labels created after the time you've specified will have the next day's ship date, rather than today's.