There are interposition arthroplasties that can be done if the joint is stable. This means taking a tendon and rolling it up, and stuffing it in the space where the arthritic joint is. If a fusion is necessary, usually there is no loss of function, since the motion lost at the mcp joint is made up by the surrounding joints. I would suggest a visit to an orthopedic hand specialist to explore your options more closely.
Its the metacarpophalangeal thumb joint