Quoted:
Where is haLfLiFe when you need him?
Right here Sir, one of the links you placed is from the Swiss Rifle Message Board. A solid source of knowledge who posted in that thread was Gusian who is a current Swiss soldier.
Gusian says
"It is not certain if there was a period that both beech and walnut were used. What we do know is that often later serialed (=younger) K31's have a walnut stock instead of beech but if these were replacements is not sure yet."
I think this as vague as it may be really says a lot. There are many younger K31's that have hit the market sporting a walnut stock when most think it should be sporting a beech stock because walnut was supposedly not available in the later K31's.
IMO from what I have read and discussed with multiple Swiss Soldiers it is not a definite answer of course, but the only conclusion(s) we can draw at this point is they were replacement NOS stocks that some received since Swiss rifles are known for being battered around by hobnail boots, or the Swiss soldier who was issued the K31 may have chosen to keep it and replaced the stock himself (I say this scenario because there were many NOS parts to be had in that time period and it would have been easy for these soldiers to get their hands on a replacement walnut stock which might have been more appealing to them since they were not issued younger K31's with walnut stocks already on them).
Swiss NOS parts are not plentiful today but they do exist. I had Gusian track me down an NOS bakelite bolt knob for my 1917 K11 since the original is cracking and falling a part. This tells me if I can in 2009 buy this NOS part that in 1954 NOS parts were more readily available to had.