Like you said, by default, the connector in a design will have its symbol based on its part number if a symbol with the part number exist. This can be enough if you have a low count of different part number, or if you only use part number families. But when you need a multiple different symbol, for a high count of available part number, this begin to be hard to maintain.
So, one solution is, to create a different library (comment symbol) for each connector style, or standard, or family. Nothing too exact, something you will be able to reuse easily for multiple part number. By example, In Mil/Aero world, we often use the Mil-Dtl connector layout standard. After that, in Capital Library, for each object type (in this case, connector) you have a Symbol tab. You add each symbol required for each part. Be sure each symbol type are in different symbol library (by example, side view are in one library, layout in another one, default symbol in another one, specification symbol in another one, etc). Once the part have multiple symbol assigned to it, when you go in the style set (Capital Project), you have a Design object, for the design, you have a Decoration and General Setting, in General Setting you have Design Setting and Library Sets. This library sets will define which symbol library will be available to your design. So, if you only want the layout in your design, you only have to create a library set that contain the layout symbol library (+ the library that contain your default symbol). Then, in the style set, under the Connector-Decoration-Symbol, you add a symbol, select the option "Auto-Select by part number", then you select the default symbol (if a symbol is missing, this symbol will appear).
Like this, your symbol selection will be driven by the applicable style set. If you didn't set this in the style set, on the design, you have access to right click on the object, and select the option to take the next symbol, the part will cycle the symbol assigned in its Part Library Symbol tabs.