Most of the methods I saw involved donor carts
Well, while from your wording you may not be a fan of that (neither am I), opening a game of the same region/mapper and replacing the roms IS easier, cheaper for very small volumes, (and possibly resulting in better build quality, at least on the outside)...
Else, you would need a new plastic shell (preferably of decent material and tolerances),
a new circuit board (and I think the NES at least uses a non-standard pitch for the console connector, which may complicate the matter if not going full DIY with etching and drilling),
a new mapper (doable with discrete logic ones - though buying chips 1 or 4 at a time is likely inefficient - not so much for proprietary ones: you could fall back in the previous case by imitating them with a fpga or the like, but again prices for small numbers are far from competitive),
a new security chip (there are 3rd party alternatives like the CiClone, or Krikzz's allegedly open source AVR port of the Tengen clone)
etc etc...
All doable but needs some planning and design work!