Firstly,about stored procedure execution needs partition key.You could find the below clear statements in the link:
If a stored procedure is associated with an Azure Cosmos container,
then the stored procedure is executed in the transaction scope of a
logical partition key. Each stored procedure execution must include a
logical partition key value that corresponds to the scope of the
transaction. For more information, see Azure Cosmos DB partitioning
article.
Secondly,in the past,you could create non-partitioned collection on the portal.But now, you can't.Please see my previous case:Is it still a good idea to create comos db collection without partition key?. Based on your description,you don't want partitioned collection.So, please create non-partitioned collection by Cosmos DB SDK. Such as:
DocumentCollection collection = new DocumentCollection();
collection.set("id","jay");
ResourceResponse<DocumentCollection> createColl = client.createCollection("dbs/db",collection,null);