Maybe someone actually has a good reference from the period as to what wood was used. But what you should use ought to be a different question: a working replica of any old, possibly dangerous machine should be, above all, safe to operate. Authenticity is good, but secondary. People who make repro early steam engines will put modern safety valves and gauges on them, and use modern gaskets. The specific question of what you should use is a pretty good one to post ( no pun intended) on a timber-framers' chatroom - I know a few have built them. My guess is that for at least the arm they'll say the species of wood will be less important than the quality- i.e. straight-grained, with few significant defects