I'm sorry for the slow reply. If you are selling services, I strongly recommend trying the Appointments feature; this allows you to let your customers book appointments or class reservations, and collect payment (or not, it's configurable). More detail on features and how to set this up here: https://www.godaddy.com/help/add-online-appointments-section-27307?.
The online store does not currently support downloadable products or services, so there is not a way to remove mentions of shipping from the current product. We are looking into supporting digital downloads, which would also involve removing shipping from the presentation, but we do not yet have a schedule for that feature. I apologize that we don't have the capability you're asking for - but please let us know if the Appointments feature doesn't meet your needs.
heidi, GoDaddy product manager