I don't think I've ever seen wood used around copper coils but have see some materials that look like wood.
Composite Materials: Some older electrical equipment might use composite materials designed to mimic wood while providing better durability, heat resistance, or electrical insulation properties. These materials can include fiberglass or resin-based composites.
Phenolic Resin: This is a type of plastic that can be cast into shapes resembling wood. It is often used in electrical applications due to its good insulating properties and resistance to heat.
Thermoplastic Insulations: Some welders and electrical devices use thermoplastics or thermosetting plastics that can resemble wood in appearance and provide good electrical insulating properties.
Wood-Like Synthetic Insulations: There are insulative materials that can be designed to mimic the texture and appearance of wood while being made from synthetic compounds.
The Monarc welder sounds good considering how long it's lasted.
My oldest arc welder is a Samson ,I think it looks from about the sixties ,I see a pic online of a similar one below.
The old welders are very heavy ,probably worth more is scrap than what you can sell them for working..