George,
Welcome to the QB.
From the eBay picture your machine looks to be a model 66-18. I have three of them. I like them a lot.
I wouldn't let the entire machine soak in kerosene as I don't know what effect that would have on the crinkle paint.
I've had excellent results using sewing machine oil with a tooth brush and cotton balls cleaning my crinkle machines. I have a bunch of them.
Letting the under side soak in the kerosene is fine, I'm just not sure of the painted parts.
I "think" the veneer on the case is either walnut or oak. I have one that has been stripped of it's stain and it looks like walnut to me. But I'm not a wood X-spurt.
I get my veneer from a local furniture manufacturing store. But I have seen on line sources. Unfortunately with the last computer crash I lost those links. Perhaps a search for veneer for sale might get some results. Or one of the other forum members might have the links.
Joe