RR - per your hypothesis, NO, absolutely not!!! There is no prima facia correlation of shot charge/slug weight and peak pressure. Your gun's action and barrels are interested in peak pressure. The elcheapo shells are intended to cycle semi-autos and do not take older doubles into consideration. If you are going to feed older doubles, you are going to have to use shells that are KNOWN to produce lower peak pressure. This generally means "specialty" shells or purpose made reloads (ones with low pressure).
The wood part of your guns are intersted in recoil force. You can safely estimate recoil force as a function of shot charge weight and velocity per above.
The care and feeding of older guns requires low pressure, light recoil, and good lube kept clean.
