In my certification work, I do not [yet] work with the ASTM nor MOSAIC standards. I'm not familiar with those standards, nor the standards applicable to non certified airplanes. But, I do know that physics don't change because of how the airplane has been authorized to fly. The Part 23, 33, & 35 certification standards are very well thought out, and the result of some painful and expensive lessons. If you need to "do it differently" from those standards, you really want to consider all of the implications.
While doing flight testing for propeller change STC approvals on GA airplanes, I have found a few things which were pretty important to understand, and could be an indicator of a reduction of safety, if not correctly compensated or mitigated. In my flight testing of a Bellanca Scout, I found that replacing the metal propeller with a composite propeller allowed airframe and in particular, horizontal stabilizer vibration which was worrisome. I researched this and found a report of similar observations with a composite propeller change to a Citabria in England in 1992. That could be an unsafe condition, as on those airframes, the metal propeller acted as a "harmonic balancer" for the whole airplane, and when it was taken away, undesirable vibrations were possible.
As I have mentioned, a propeller change can dramatically change the gliding characteristics of the plane. If the characteristics have been changed, this needs to be understood from results of good flight testing, so that pilots know what to expect, and how to handle the plane in the case of engine failure
Composite propellers (including wood) are generally not subject to installation limitations to engines the way metal propellers are, though having a good understanding of any vibration vulnerabilities is still important. There have been a lot of hard lessons learned, some over longer than obvious periods of time, in the realm of propeller vibration, so it's worth understanding well for the combination you propose.