There was a Canadian that made replacement wood for Chevrolet steering wheels some time ago. I haven't seen any mention of that for many years so don't know if they are still being made. 

If you have one section of the steering wheel to use as a template, maybe a local high school wood shop could make you some new ones.

Another possibility is to talk to the Laney College wood shop teacher, which is near you  in Oakland.

Good luck!  Dean

@lou-macmillan Lou, is the finished rim round or is it 8 sided with rounded corners?

Mike

    The 23 steering wheel that I glued together was a rounded octagon.  I believe the 27 is more circular and may have 8 or 6 pieces.   All I have is four spokes and aluminum decoration around the horn button.    

    Thank you for your input,   Lou        

I can verify that Lurch's steering wheel ('27) and Justin's steering wheel ('28) are both circular.

Dean

@lou-macmillan Lou, I have these.The complete wheel is a Chevy but I don't know the year.

The ring is 12 sided. They are both close to 17 inch diameter. The picture was not well posed.

Mike

@35mike 

That complete wheel won't work on my truck (1940)...but it sure is pretty! (Just jumping in here because I really think it is nice looking!)

    FYI:  1937 and older Chevys used a taper-key connection between the wheel and shaft.   1938 and newer used splines.       

A 28 Sedan has 8 wooden dovetail sections.  It is 17" diameter and circular with finger lumps behind.   Many years ago, I recall holding two of the wooden sections when turning my first corner in my 27 LM that were no longer connected to the metal spokes.