If a chatter file has been shared then SalesForce creates a URL which is public. How can I get that URL using REST APIs but not chatter APIs? I want to do so because quota of chatter API calls is far less per user per hour and I want to get URLs of large number files which are public.
As per the comments, try using the ContentDistribution API and the corresponding DistributionPublicUrl field.
Use to following SOQL to get public URL of the required ContentDocument: