Porting from the Wii or the PSOne is a complex and involved task that can be broken down into multiple separate engineering efforts working in parallel to produce a working end product. The best possible thing you can do before moving to the target hardware is to compartmentalize all of the non-portable code while ensuring that the game continues to run as expected. When you commit to moving to the new platform, your effort switches to reimplementing the non-portable compartmentalized parts.
So, to answer your question, yes, you will need to become or work with a Sony and Nintendo licensed developer in order to take this approach. In the case of Sony, I don't even know if they offer a PSOne development program anymore which presents issues. Your Sony account rep can help clarify.
The major subsystems that are likely to be the focus of your porting effort are:
- Rendering Graphics code contains fundamental assumptions about the hardware it is being run on in order to perform optimally. API-level compatibility is superficial compatibility and does not get you as much as you may hope it does. Plan on finding the entry point to the renderer and determining what data you need to render a scene and rewriting all the render code from there for your target hardware.
- Game Saving Game state serialization and archival will need to be separated out. Older games often fwrite() structs with #pragma packed fields. Is that still going to work for you?
- Networking Wii games write to high level services that are unavailable on your target hardware. At the low level, sockets are still sockets. What network services do your Wii games rely on?
- Controls From where you are coming from to where you are going, anything short of a full redesign or reimagining of input will result in poor reviews of the software.
- Memory Management Console games often make fundamental assumptions about the rate the system software returns memory from the heap, how much fragmentation it will cause and the duration the game needs to operate under these conditions. These memory management assumptions are obsolete on the new platform. It is wise to write your own memory manager that provides a cushion from the operating system. Also, console games compiled for release are stripped of most error handling and don't gracefully handle running out of memory-- just a heads up.
- Content Your bottleneck will be system memory. Can you fit the necessary assets into memory? With textures, you can reduce mip where necessary and with graphics hardware timing, you can pull in the far clipping plane. With assets resident in memory, you may need a technical artist to go through and reduce the face density of your models or an animation programmer to implement a more size-friendly animation codec. This is very game specific.
You also run into the standard set of problems with things like bit compatibility (though the Wii and PSOne are both 32-bit), compiler idiosyncrasies, build script incompatibilities and proprietary compiler extensions.
Games are relatively challenging to test. A good rule of thumb is you want to have enough testers on your team to run through the game in a maximum of two days, covering all major aspects of play. In games that take a long time to beat (RPGs with 30+ hours of gameplay), your testing team needs to be quite large to offer full coverage. Because you are just doing a port, you can come up with a testing plan that maximizes coverage of your new code without having a testing team punch every wall in your game to make sure it (still) has clipping. The game shipped once.
Becoming a licensed developer requires you to apply. The turnaround time, from experience, is not good. Generally speaking, priority is given to studios with shipped titles and organized offices with reasonably good security and the ability to buy the (relatively) expensive development kits. You may be better off working with a licensed developer if you do not meet these criteria.
Console and game development is challenging for people already experienced in it. There is no book that covers it all. My recommendation is to attempt to recruit an expert who has experience shipping titles in a position of systems or engine programmer. What types of programmers and skillsets exist in games is a whole different question for Stack, though.