the below assumes that you have realized the this MUST be a switcher.

This means, that I have to decide on the exact ICs capacitor sresistors etc. right form the word go (After the conceptual design is done)
as far as mechanical size yes. In a case of questionable component availability of e.g. an inductor, you can 'double pad' so two different ones can be used.

Secondly, I could get a wood casing fabricated (because from where I come it is easier to get a carpenter to do one for me) with an internal layout similar to the final product and do all prototyping on top of that. I hope the casing does not have much effect on the performance. performnce, probably not (it will change the thermodynamics) but re EMI it sure will.

Finally the question, why would a charger be sensitive to layout? Is it because of the use of a transformer? maybe, but mainly because a wire is not a wire but a series of inductors with capacitances to everything else. I have seen transistors heat to blow in a faulty laid out switcher prototype

And again, are there alternatives to using relays and transformers?
relays??? you NEED a transformer or some customers will be schocked.

Erik