Just wipe with a soft clorth moistened with mineral spirits.
Linda C

Nicotine is basically an oil ... I wash with warm soapy water, and dry it thoroughly with a fresh cloth.

Then I wax and buff.

Wear cloves: nicotine can soak through your skin and make you really sick.

I avoid water on antique furniture at all costs...if the finish is laquer or shellac water will cloud the finish.
Nicotine is not an oil....but the smoke from tobacco can seem oily. Nicotine is water soluable....smoke stains are often oil based.
Nicotine soak through to your skin from washing smoke stains off of furniture??? I really don't think that is a problem.
You are not dealing with nicotine, but rather with smoke stains. Treat them like any oily stain. Mineral spirits is the safest way.