Hi Spiros,
As long as you can display the relevant raw data, for example NDB or VOR needles, I would suggest that if the approach is not in the database, you construct a simple FMS final approach course. That way you can fly the final approach in LNAV, while monitoring the raw data via the needles. This will provide a much lower workload and a stable lateral profile, enabling you to devote more attention to the vertical profile.
How you construct this final approach course depends on the situation. For example; if the final approach course is aligned with the runway, you might be able to construct a 'Runway Extension' at a certain distance from the threshold. Some FMSs have this feature and it provides a relatively easy way to construct an extension to the runway centreline. If you can't do this you could define the final approach course towards or away from the beacon by using the 'Place bearing/distance' method of constructing waypoints. This does amount to 'map building' and may be frowned upon by some authorities.
Another simple method is to wait until you are approaching the final course and then to go 'Direct to' the relevant beacon, making sure that you type in the correct DTK (Desired Track) or course (CRS) before you execute. Some FMSs refer to this as 'PVOR' (Pseudo VOR) or 'OBS' (Omni Bearing Selector) mode.
There will be some who say, "What if you enter the wrong inbound course?"
My answer is that the same cross-checking skills are used and the same potential errors could occur when you are setting the raw data on a VOR approach using an HSI or an FMS course Line-Select Key. Both pilots must cross-check the inputs and the results must be checked against charts, common sense, etc.
Remember, in all this you are still displaying and monitoring the raw data, so it could be described as a 'raw data' approach with LNAV stabilisation.
As far as the vertical profile is concerned, I would use VS if the autopilot is capable of displaying the selected rate.
As to the missed approach, if the approach is not in the database you will have to fly this using HDG, but even here a simple depiction on the EFIS MAP of some relevant points may improve situational awareness.
With reference to 'the rules' about databases, etc., my understanding is that you must indeed fly an RNAV (GNSS/GPS) approach from a database-selected procedure, without modification. I don't believe there are any rules about using the FMS as described above to support conventional non-precision approaches. I did exactly this whilst being observed by a UK CAA Flight Operations Inspector and he had no comment to make. As always, it's a matter of knowing what you're doing with the equipment and keeping in mind any limitations thereof.
Hope this helps.