Using Gojo to clean old wooden chairs, clocks?

My dad gave me two very old Winsted, CT (where I was born) made chairs, very similar to Hitchcock, and an old Gilbert clock (also made in Winsted). They've all been in the attic for a very long time, and are pretty dirty, not just surface grime. Someone mentioned applying a good layer of Gojo, the handcleaner stuff, letting it sit for a while, and then cleaning gently with a fine steel wool. We're still nervous about doing that, especially on the stencilled areas of the chairs. Anybody heard of this technique, or have any suggestions for us? Thanks!