Declarative: Add an additional user license (for Salesforce & Skuid). You can go about configuring a second Salesforce data source (follow this Salesforce doc) that points to your same org with the user credentials hard coded. However, it is important that you make sure this user ONLY has the permissions that they absolutely need. You can then use this data source on your public page. Note: This method requires an additional paid Salesforce user and Skuid license to accomplish.
Use triggers as described here.
Write Apex code that runs in “system mode” to get around the Salesforce security model. You will need to use Skuid’s model API on the Skuid page.